The 2 black wires going to base plate are being used as an earth ground... this plate should only ever be run to ground and seeing as it also has a green ground wire attached, id say its been used as a ground path.

You can safely join the 2 purple wires together with no issues.. you may be right, it may have just been cut to join to the white/yellow.

The black wire going to the timer can be pissed off altogether from the switch... looks like its being used as a neutral.
Green/Blue just snip off from the switch... this is now the whole relay taken out off circuit.

Im guessing here, but it looks like someone has added a 240V 30sec delay timer to the flippers ( Green/Black)... is this the power train to both flippers?