Hot Start Problem - Fix #1
The 7er with automatic transmissions suffer from hot start problems. The problem is not the starter per se, but the starter solenoid refusing to engage. Some owners fix this issue by pouring water over the starter solenoid until it is cool enough to operate. It appears that the extra wiring in the starter circuit of the automatics (additional electrical resistance) combined with the hot starter solenoid produces marginal operating conditions.
One possible cure is to obtain a used fuel injector relay holder, so this way it looks as it belongs to the car, (as in factory look) then follow hook up diagram below.