No telling exactly how things are wired with all the changes its been through.
These seat belt interlocks are a mystery to me. Never dealt with one directly.
If you want to turn the starter over you could bypass the existing wiring and run a wire from terminal #50 on the back of your ignition switch to terminal #50 on your starter.
Back of ignition switch -
That your gauges light up in HALT but not in the RUN position may be due to a faulty ignition switch or incorrect wiring at the ignition switch.
Here's a link to a late 2002 schematic that you can download and print out. Instead of trying to get the seat belt interlock circuits to work - bypass it.
http://www.bmw2002faq.com/component/option,com_forum/Itemid,50/page,viewtopic/t,316840/