US LKM have only 3 relays
dip light, high beam, foglights.
Only EURO version has 4 relays, the no. 4 is for the rear foglights.
A EURO LKM will also work on a US version, I have a spare one here from Germany and tested it, in Japan we also do not have a rear foglight.
Only prob was, that I got the CC warning for the foglights, but it worked.
Delay on a standard LKM is not normal. I can imagine, that the contacts are sticking on the low beam relay in the LKM, the low beam relay has 2 contacts and 2 fuses.
Open up the LKM, and clean the contacts inside with fine emery paper, maybe even re-bend them.Shogun E32 Tech Tips: http://twrite.org/shogunnew/topmenu.html
Re: US LKM have only 3 relays for the E32/7series
manufatcured by Hella, most all e34s between 1988 and 1992 have LKMs made by Hella and have 4 relays. The E32 LKMs have 3 and came in two types- LKM and LKM-B (basic). Only the E32 LKMs have a Mustard relay. Both LKMs are interchangeable E32/E34. In 1992 Hella changed the circut protocall to match the newer DME upgrade.