Can you please advise Chassis Number of your SS-Jaguar.
There is a lot of differences across the 1936 to 1938 period re Lucas matters (wiring diagrams etc) and Tool Kits/Tool Trays. I can help you with most of the variations, just need to focus on what exactly, as just saying a 1937 Saloon may not be enough.
Indeed it would help my detailed research into SS-Jaguar Tool Kits if you could provide photos of your current tool tray and indeed any photos you may have of any tools. Can you please email me direct at firstname.lastname@example.org and attach photos. What I can provide re Lucas information and Tool Tray/Kits is potentially many MB and far to much to tie up this web site.
Just as a guide - 1936MY and 1937MY have different tool trays, and indeed 1-1/2 litre is different for both relative to 2-1/2 litre. 1938MY to 1940MY have four different tool trays but now the 1-1/2 litre is the same as 2-1/2 and 3-1/2 litre. Above applies to Saloon and DHC. Tourer has a totally different tool tray arrangement, and SS100 actually has a Tool-Roll that is stowed in a metal tool-box underneath the passenger floor, along with Jack, Tyre Pump, Hammer. So chassis number is important, as my MY comments are approximate.