It may not be the pump. There is a "demand limit" that prevents the pump from running and running if a hose were to break somewhere. I think the maximum time the pump will cycle for any request, whether that be door lock, door unlock, trunk grip extend, trunk grip retract, headrest retract, lumbar inflate, or trunk pull down release (the mechanism actually assists the trunk pull down in some fashion) is 30 seconds. It may be that once that limit is reached, the system "kicks the offender off the island". There may be a certain number of times this limit must occur for each sub-system, but possibly not. (That is the case with the closing assist).

The reason I say this is that my lumbar bladders were ruptured, but no matter what I did with the switches on the seats, the pump never cycled on to provide pressure. Once I pulled/replaced the power, it would continually try to reinflate the busted bladders until the time limit was reached, then it would quit trying forever. This may not be the case with the central locking system, but I'm sure this was the situation with the lumbar supports.

Try pulling the power to the pump for about 10 seconds and see what starts working (or not, if I'm wrong.)

The system has certain pressure parameters it expects for each task requested of it. For instance, if you request door lock and there's a slow leak in one of the actuators, the max pressure for that system won't be reached in the required amount of time and that will trigger a DTC.

On my '92 300SE, I had trouble with the actuators for both the driver front and rear door locks. I'd get a DTC for "Central Locking System Air Demand Too High". I checked the actuators (easy to get out the rear doors - PITA on the front) and they both leaked air on the pressure cycle. Several of the tabs that hold the units together had cracked and the suckers would leak air under pressure - but they worked just fine under vacuum. I fixed the problem by disassembling them CAREFULLY and spreading some silicone grease (NOT axle grease) on the diaphragm sealing surfaces, then using some zip-ties to hog-tie the actuators back together. Working just fine - look like heck, but when the door panels go back on, who's gonna see?

Good luck.