During last 9 years on 3 separate forums for k1200RS / K1200LT , I have seen many cases related to Cruise-Control, HOWEVER you are the 1st one that cannot get a SET light at the 1st step of the diagnostic procedure (Push-Hold SET button, THEN turn Ignition ON).
Do you have other dash warning bulb that are not going ON after you turn ignition ON ??
Assuming dash is working OK , you should see engine coolant temp-warning , Oil-pressure and Alternator (until engine is started). You should also see the low-fuel warning flash for 1 or 2 seconds.
In the "Most probable cause" that will need more tests and research:
1) Burned SET bulb (same small bulb as all other warnings , except ABS, so you can swap for a test). See attached image...
2) the SET button is defective (or making bad contact) inside the main left combo switch. Cruise function buttons go to a 6 pins connector located inside the relay junction box lower panel (not easy to reach). This allows usage of Multi-meter continuity function (Ohms) to check all 3 buttons for cruise function (ON-OFF , SET, RES).
There is a write-up on this forum on how to open the Left switch (with pictures). First time you do this job requires a lot of patience to remove and open the switch assy. See this thread, about 3/4 down for a post with 9 pictures:
https://www.bmwlt.com/forums/k1200lt/53849-flaky-cruise-control.html
3) there is a bad or loose connection at the main 10 pins connector of the cruise-control unit (this is much easier to reach than the left combo switch).
ALSO, in the "Not very probable , but possible" causes:
4) a failure of the main Cruise-control unit (not very probable)
5) you have done some recent electrical work that may have affected wiring
6) mouse has chewed up some wiring (we see more and more of these issues here with bikes not being ridden much)