hi,
on the 5-series Toyota the signal to the LPG lockoff solenoid comes from what is called a "rev box" which sees an input from the distributor and converts it to a signal to trigger the rev box relay which in turn, opens the lockoff solenoid. the most common failure point after wiring is the rev box relay. the rev box itself rarely fails.
the rev box and rev box relay can be found bolted to a plate either between the battery and the front panel of the engine hood next to the fuse receptacle, or tucked between the battery and the LH overhead guard rear leg, under the LH engine hood hinge. The rev box is a brown plastic box containing a small circuit board. the rev box relay is a small canister resembling a turn signal flasher, with a grey plastic four-spade rectangular connector.
if the wiring is OK and replacing the rev box relay fails to solve your problem, the next cheapest solution is to switch power to the lockoff solenoid through a manifold vacuum switch.

According to my data, that appears to be correct. There is an LPG switch in between the key and the solenoid but that's about it.

They just by-passed a faulty harness.