I don't think Silvers get fast track at all airports and as you say it varies.
I believe it's only an actual published benefit for LHR, LGW and JFK.
See this thread but here's what it says re GVA. Perhaps a regular can give an accurate update.
Tracking BA Fast Track and Priority Boarding
I've no idea if that works but this is from the Fast Track Thread (See the Wiki)
GVA - Geneva Boarding: Boarding: Yes. Security: Yes (requires scanning of BP - no non-status guests in Y. If status in Y, or CE on BACF, you'll need a BP printed at the check-in counter; app and home-printed BPs do not currently work).
Pete