Another non-flying station with a gate guardian is RAF Brampton with its F-4. RAF Henlow has a Hunter; whilst Henlow does actually have a runway, it's made of grass.
When I was at RAF Staxton Wold in the early 90s the then CO briefly entertained ideas of asking for one of the F-4s then being retired to go on the gate. Whilst there would at least have been an AD connection I think the project foundered on the sheer amount of paperwork required.
One of my later jobs involved occasional visits to RAF Croughton, the USAF comms hub north of Oxford. Again, a non-flying site (although it was an operational airfield in WW2) it has an F-105 on the way in.