Williams did this fuse arrangement for GI on a lot of games. There are 4 separate branch circuits for the GI current to go to different parts of the game. Each branch has a fused striped colored wire, essentially the "hot" side of the AC voltage, and a corresponding solid color return wire. For example, purple striped wire will go to one side of a string of bulb sockets, and the solid purple goes to the other side (and this may be the solid color attached to a stapled bare wire running from socket to socket)

So first you need to repair the problem that is causing fuses to blow. Most of the time this is a bad socket. Focus your attention on one string or another first. You have a white/yellow sting that has a problem, and a white/violet string that is a problem. Remove all the bulbs and use a dmm/voltmeter to test for shorts between the sockets would be the first thing to do.

All four positions should have 5a slow blow fuses installed, and each controls a string of the gi. In the pic, those appear to be different value fuses. Were the blown fuses the correct rating?

Probably not a large problem, usually these are small problems that can take a lot of patience to find. For the playfield GI, look carefully for sockets that are shorting to adjacent things. Especially near the perimeter of the playfield, sometimes these are bent and touch the side rails when the playfield is lifted.