While I am not familiar with the particulars of a '90 GSPD, some detective work might be revealing. What other things typically happen, electrically speaking, when you push the "start" button?, apart from the starter motor engaging. If the relay fires when you hit start, it is trying to turn something on or off. A "load shedding" relay perhaps. Does the relay appear to be OEM, or a feature that was added after assembly? Does the wiring diagram provide any clues?

Not 100% sure, but lots of BMWs turn the headlamp OFF during engine start since the HL is a major consumer of battery resources. Trace out the wires in the schematic and see.

Thanks for both replies, I took a look after work today with a wiring diagram this time. It looks like the grey relay IS the starter relay while the orange relay that I thought was for the starter is actually the headlamp relay It is likely clicking in unison with the starter relay as it shuts the headlamp circuit during starting. Just waiting on a solenoid and I should be back in business.

Typically, BMW wants about $30 for those relays. However, you can sometimes Google the manufacturer's part number on the can and find them cheaper on Amazon. Not all relays, but some. Quite a few are in general use on cars with multiple manufacturing sources. Those "mini-can" relays are very popular with auto makers.

If you find a possible substitute on the web, it is very important that you compare the schematic on the side of your relay very closely with the schematic pictured on your web source to be sure they are electrically identical.

My old starter relay

My $7 replacement starter relay

Notice that the plastic mounting arm (pictured on my new relay) is an option not needed for the motorcycle, but one that does not affect the electrical operation of the relay. So I simply sawed it off and saved the $23.