The flashers going off in coil test is normal. As flashers are part of that test. The relay is also part of the high power circuit. Are you sure you don't have a plug in the wrong way, wrong spot or backwards. The coindoor switch should only turn on the high power relay when pushed in or pulled out.
Because it's turning off your G.I. I think you have a bad G.I relay. Or possibly a plug in backwards or on the wrong connector. Check the schematics for wire colors and pin outs on your boards. And check the G.I relay. It is probably bad or has cold solider joints.
GI Power comes from the transformer.
GI Power goes to the power supply board through an input molex plug.
GI power goes to a relay on the power supply board. This relay can be activated to turn on and off the GI.
GI power leaves the power supply board through an output molex plug.
GI Power goes into the PPB board through an input molex plug.
GI Power goes through a fuse (and potentially cracked fuse holders!).
GI Power leaves the PPB board through an output molex plug, and goes to the backbox or playfield.
Power Supply board relay RY1: this relay controls the GI (General Illumination), and is controlled by CPU transistor Q28 (TIP122). It is very common for this relay to have cold solder joints, or to have relay switch contacts that are melted together. This relay is a 24 vdc 10 amp relay with two DPDT switches. There are a total of 8 solder points on this relay; two connect to the winding of the relay coil (to turn the relay on and off). The other six contacts (two distinct sets of three contact DPDT switches) are the relay switches. Source number FRL264 P024/02CK, Sega part 190-5003-00.
All of the relays used in DataEast/Sega games have at least two sets of contacts. If a relay is mistakenly replaced with (for example) a single set of DPDT contacts, it could short the power supply and start it on fire!
On all DataEast/Sega power supply revisions, connector CN4 directs 18 volts (CPU controlled lamps) and 32 volts (solenoids) to the game. This connector is twelve pins, and has NO key pin. If connector CN4 is removed, it is very easy to replace the connector housing shifted one pin to the right or left! This will immediately blow either the 18 volt lamp fuse or 32 volt solenoid fuse, which are both bolted to the rear of the backbox.