Found this, not sure how definitive it is but more or less echoes what I wrote above but in more detail ( I was wrong about JBL but ballpark sort of tone )
The following is what Jake E Lee used for the recording of The Ultimate Sin.
For pickups Jake used two Dimarzio SDS-1 and an Seymour Duncan Allan Holdsworth prototype hum.
For his amps, he used a 1977 Marshall 100 watt head (stock) and a Marshall 50 watt head (circa 1964) with a straight Marshall 4X12 cab with EV speakers. Jake normally doubles and triple-tracks all his rhythm parts (Rock'N'Roll Rebel had four). All of the solos on The Ultimate Sin were played through the Marshall 50 watt with the exception of "Killer Of Giants", which was performed with an old Rockman and a Rat distortion pedal.
Jake used an array of Boss units, including: CE-3 Chorus; BF-2 Flanger; DM-2 Delay (rhythm); (2) DD-2 Digital Delays (lead); GE-7 Eq; SCC-700 computerized pedalboard; and a Variac (set between 90 and 1100) . The two digital units are set as follows; one for slow leads and a lot of delay; and one for normal leads with just a touch of delay.
Jake used a Boss OD-1 Overdrive to boost his Marshall amps and eliminate an unwanted low frequency when he cranked the bass control on his Marshalls. On the Boss OD-1, Jake turned up the Drive to approx. 9 o'clock and the Level to maximum.
Jake used Fender .121 picks. His string guage was .009; .012; .017; .026; .036; and .048.
The clean parts during the verses on "Shot In The Dark" are a 1957 Fender strat through a Roland Jazz Chorus amp.
The acoustics on The Ultimate Sin were an old Martin steel-string and a cheap nylon string which "happened to stay in tune".