At the relay socket? The starter motor should run only for as long as it's being jumped by you. It's the PCM that does the thing where it keeps cranking until it starts even though you let go of the key after flicking it to start. The PCM does that through the - signal wire to the starter relay.
Hold it... I missed this... I am slow. You are saying you not getting "the check bulb sequence" on the IPC when you attempt a crank? That is not correct operation.I should add, the things I know I don't have are:
The bulb check lights when key is turned to crank
Blower motor won't turn on