blue indication still on, yes I would say is the High beam relay from the LKM.
You have a new one, just open it, if it looks dirty, just carefully clean with soapy water, avoid water in open devices, rinse and dry with warm air, close and plug in place. New junkyard LKM may have worse bugs that the one you have!!
The proposed fix in Bruno's site
http://www.bmwe34.net/e34main/mainte...trical/LKM.htm
is very simple and easy to carry out, what you have to look after, is what is connected between pin 2 and pin 20 of the LKM (Relay contact) see picture for pin ID.
Javier