87 Toyota pickup 22re, injector test while installed but not hooked up to the harness. starts but dies after a couple seconds. cold start injector working fine.

If the injectors are not firing I assume that you plugged a light into one of the injector connectors and there is no flashing light while cranking, each injector has to have a supply voltage to one of the wires in the connector, this may be battery voltage or a lesser voltage of around 8 volts, the earlier systems used a resistor to drop the supply voltage, in either case there should be voltage to one wire with the key on, if this is the case plug your test light into the connector and see if it flashes while cranking the engine, if the light does not flash the problem may be the computer, the computer switches the injectors off and on by breaking the ground connection inside the computer .
The computer may not be the problem it may shut down because an input signal is missing so it's important to check for diagnostic codes first by using the check connector under the hood using a jumper wire between terminals TE1 and E1.