I think I have worked out your failure mode now (hindsight - a wonderful thing)...
Let us assume that the switch feeding the AC voltage supply to EP104 fails and goes open circuit.
In this case, you will not measure any AC voltage at EP104 (relative to EP105), but will on EP106. I would have thought - with this failure mode - the the Vectrex should still have worked - even though it may have been a bit 'ropey'. Both DC supply rails (+ and - 9V) should be present - but only the half-wave rectified versions rather than the full-wave.
If you now join EP104 to EP106 with a piece of wire - the Vectrex (to my way of thinking) would still only work in the same way as previously.
Anyhow, in this case, the fuse should not blow.
If the switch (after a period of time) then started to work and conduct once again - you would then either have a direct short circuit across the secondary windings of the transformer - or a high current flow in the secondary windings of the transformer (depending upon the resistance of the partially working/faulty switch). In this case, once the current exceeded the rating of the fuse, it would blow.
That is my current thought of course.
You can repair these switches by taking them apart. But, watch the videos first! They contain little springs that jump out if you are not careful... You will also need the photographs of how to reassemble the parts.
If the switches can't be repaired, the best thing to do would be to unsolder the wires from the switch totally and connect the wires together correctly (using solder and some heatshrink tubing) and affix a label to the case indicating that the ON/OFF switch is inoperable and that the unit should be unplugged from the mains when not in use.