I had wondered about the clogged exhaust, but (1) she has only 90K miles and (2) as I posted earlier about “condensation” blowing out her exhausts (as it just turned out to be, fortunately 
) the output of both exhaust pipes was visibly substantial, equal and continuous, so it appears the system is still flowing through smoothly. 
The factory repair manual lit. mentions other possible causes of fried valves is (1) the air pump not working/failure (e.g. broken or missing belt) (2) malfunctioning switching valve, among other causes … 
I guess what #1 means is that if the pump should ever stop pumping while the car is running, that condition would allow the hot exhaust gases to go through into the system, since there is no countervailing air pressure from the pump to prevent that from happening … ? 
As mentioned, the diverter valve only passes pump air to the air rails for a short period of time during warm up. After that, the diverter valve passes the pump air into the RH air cleaner box. If there is back flow of exhaust gasses from the air rails, it will ultimately go to the air pump and possibly cook it if over a period of time if there is sufficient volume of heat and flow. I guess luck in this case would be to have clogged air injection tubes and passages in the heads.
Let him try and see what happens to electrical tape and exhaust heat - you learn something new every day.
Hmmmm … Come to think of it, maybe that high heat (i.e. manifold) tape, then, Gregmatic? 
I wondered what the 12 little tubes mentioned earlier led to. So are they actually metal tubes? I guess if one were to remove the system it would be possible to plug up those holes with metal epoxy putty, e.g. QuikSteel? Or, maybe just as simply, remove the “Y” hose and plug up the two ends of the air rail with the putty? … I was also wondering if we just disconnected the pump (or the belt, if it only goes to the pump). As long as the diverter valve is good, I guess that would work, but if not the hot gasses would be cooking the 2 valves again, correct?
Yes, the 12 tubes are mettalic, and are known to corrode to the extent that they begin leaking exhaust gas if the internal passages are not clogged. As to other options, read pages 312 to 314 of Kirbert’s book “XJS Help”…
OOOPS. make that “Experience in a Book”
“Help for the Jaguar XJS Owner”
Offhand, I wonder why Jaguar changed that plumbing. The old system was all metal except for some hard plastic in the tee. Why would they replace that with a Y-shaped rubber hose? That seems like a retrograde step to me.
I was wondering too about parts of that system, Palmdude … I didn’t think Jag was into “planned obsolescence”, but maybe they were … (?) 
Well, a bit of bad news … It looks like after I ordered one of the one-way valves (i.e. the other one) from Welsh’s website catalog they turned around and cancelled it. WTH? 
Their parts guy apologized to me and said that the part should not have been listed in their catalog as available, as it is in fact N.L.A., even to them (as all the other vendors had told me). 
He said he would try to find me a good used one (same for a “Y” hose), but that was the last I heard from him …
So, what do I do now, if he can’t find a good used one? I’m wondering if things would be O.K. if I disconnected the belt to the air pump (if it only drives the air pump! ?), which should also reduce some load on the engine, and plug up the end of the air rail that is missing a valve. My tech guy said he should be able to find a metal cap for it that is the same size and thread as the valve. My thought though is just goop it over with an epoxy metal putty, e.g. KwikSteel… Does it sound like that would work? I guess this plan is assuming the air switching valve would continue to operate - sending the gases to the air filter housing. btw, how to test it, anyone?
The AIR anti-backflow check valve is pretty much a generic item used on many cars in varying shapes and sizes. I have seen ones on cars and trucks that look exactly like the ones that are used on our XJS’s. Take your old one down to some of the auto parts shops (Advance Auto, Auto Zone, NAPA, O’Reilys, etc.) I guarantee one of them will find one that looks the same and will work, though it may not be labeled for a jaguar - at a good price - much better than any jaguar parts vendor - get over the mind set that parts from Jaguar, or affiliated sources, are always better than locally equivalent parts from local auto parts. vendors.
Wow, good to know, Locker. Thanks. And yes, it was funny that just yesterday when I was at Autozone I was looking for a mechanic’s stethoscope (hoped to use it to isolate where that whistle - vacuum leak? - is coming from), and ran across a generic vacuum valve on their “Help!” line of emergency products that looked very similar to a vacuum valve we have on our XJSes. 
And of course, it was MUCH cheaper than anything we would pay for a Jag OEM v.v…
btw, don’t mean to get off topic, but the salesman at AZ sold me on the scope, but when I got home and looked at it better I noticed it was NOT the usual type of mechanic’s scope, which pretty much has a “bell” on it the same as a medical stethoscope. Instead, it has a long metal “probe” (think “dull-ended needle”) on the end of it. Near the base of the scope, the needle passes through a black rubber “ball” which the directions say is to insulate the “needle”, I guess so that the user doesn’t get the crap shocked out of them if they should happen to touch the needle probe to something with live current in it. 
The directions state that the needle can be used to search for noises created by moving parts on the engine (e.g. bearings), by transmitting the sound up the “needle” to the listener. It doesn’t look like this is useful for finding a vacuum leak. I"m thinking of taking it back (it cost $11.00), and I noticed it was taped up like it had been returned once before. Is this what they are all supposed to look like now, or should I return it for a “proper” one?
Thanks, Jim. I saw that in the factory manual as well (for the 5.3). One thing I notice Jag left out in the drawing is the hose that goes from the diverter valve to the air cleaner. 
Paul just look to see if you can pull the tubes off the bulb, that would give you a means to listen to a vacuum leak, BTW do NOT hit the probe against anything with it plugged into the lug ‘oles… it amplifies the sound exponentially.
They are very useful to listen to bearings and the like.
The single check valve used in the earlier arrangement was a standard GM part. It’s entirely possible it went out of production, forcing Jaguar to revise the design using later parts in production at the time. I seriously doubt the later twin check valves are a Jaguar-unique item.
Back when I replaced my check valves I got the Dorman 355050 valves in the mail. Funny thing I noticed - - the tube on these valves, that inserts into the y-hose, is slightly smaller outside diameter than the ones that I removed. But since the secondary air doesn’t appear to be a “critical” pressure joint, on that side of the check valve, I plan on cinching down the hose clamp
This thing seems to be about $16 from several sources:
Wow - thanks Palmdude and JimD!
Considering what JimD said, I’m wondering if there’s a different part number for a check valve with the slightly larger hose barb.