There is no relationship between your fuel pump and the ABS system - except they both use electricity but from separately fused 12 supplies. The only time you normally get both the amber ABS light and the Red Brake light is when you have no pressure (two fails - the ABS has its minimum pressure requirement, and the brake booster system has a minimum pressure requirement as well. Have you checked the ABS system fuse, and the electric pump fuse? Have you checked to see if the pump operates - or are the pump terminals and open circuit? if you have a good pump, then your can move on to checking the multi-function switch. Have you made sure there is enough fluid in the reservoir - there are a couple of switches there for low fluid level as well. If all that stuff is working, then you can move on to checking power to the ABS unit over the left rear wheel housing in the trunk. Then the wheel sensors - but, I doubt there is an ABS wheel sensor in the world that will turn on the Teves III red low boost pressure light by itself, but would likely turn on an amber ABS amber light only. But the Blink test at the ECU may also point you in the right direction.
Do you have an electrical schematic for your car?
Let us know what you find.