im not positive on how the sourcing for the relay works.
i know the tan/lt. green comes from the computer. i think it is a ground pulse (should show ground when priming, etc)
there should be red/blk coming from the inertia switch.
these two appear to be the coil wires for the relay.
Pink/blue should go from the relay to the pump. 12 volts when relay energized (or when one wire above shows 12 volts, and the other shows ground at the same time).
orange and light blue are the feed source for the pump (from the starter solenoid).
it sounds like the fusable link and/or the wire from the solenoid is bad. this is the orange and light blue wire. check the fusable link. as said, its off the solenoid. you should have juice blazing through that wire.
the fact that it is anemic would explain why the pump doesnt run (this wire is connected to the pink blue wire when the relay is energized).
go probe the fusable link on either side of it. replace as needed (it is orange and blue at the link too). should be 18 gauge link
to correct your post before the last. the fuel pump relay cant function with out power and ground. in this case, the first two i list are power and ground (when both are present, they energize or turn on the relay). then the orange and blue wire with power is connected to the wire that goes to the pump, providing power.
make sense? oh, and please use a DMM to check wires. a test light can overdraw a circuit on the computer. kinda like testing a light socket at your house by hooking an industrial air conditioner to it. way too much for the lowly house plug to handle.
good luck.