I'd pop the cover off the realay and check if the contacts are blackened , Id also check the fuel pump relay.

the TDC sensor, at the back of the engine on top of the bellhousing, check if it's cable is all rotted, It shakes a lot and oil eats the insulation. probably a good thing to go ahead and replace if you have not.

normally If you were to unplug the coil and crank the engine you should see the tach bounce each time the TDC sensor sees "once around"

there are approximately 60 or so holes int he flex plate that the TDC sensor looks at, and then a space where there are no holes.

I'd also just open the hood and start checking and cleaning every wire connection you can, look for any green looking contacts. check engine grounds. check the grounds to the fuel rail, look for two (10 mm head )bolts that hold the fuel rail to intake manifold, check those connections out really well. a bad ground will kill the injectors.
check the plug for the AMM.

you can do some wire wiggling with power on, also listen for the buzzing, If you reach a wire that when being wiggled, can change the buzzing or make it stop when you wiggle it, you might be close.

you can use a contact cleaner and and a small , new , wire brush , fine sandpaper, I have a little brush that is glass fibers that I like and when you get each one clean bright and shiny , put a bit of dielectric grease. alcohol and compressed air can help.

check your coil wires and the connections to your coil. see if the little studs look rusty on the coil. there may be an engine bay fuse near there, unplug, spray, re-seat each connector a few times. the ECU and ICU have pretty well protected plugs. You can check them. I bet it's just some bad wiring or a bad ground.

make sure your battery is ok and that the cables and grounds are all clean. a weak battery or bad battery cable or bad ground lug can easily send you off chasing geese so make sure it's not that as one of your first steps.

your alternator should have a ground wire that probably connects to the block maybe somewhere near the water-pump, I'd check and clean that ground to engine. follow the ground from the alternator to where it goes and actually disconnect it , clean it , put it back. If it goes bad your battery won't charge properly.

I don't really have anything to offer as a solution, but since the post hasn't gotten any responses I will offer a similar experience with an injection relay buzzing.

I had a 240 that had the same no start and the injection relay buzzing. I was getting 12v from the feed wire. When I jumpered the fuses the pumps would run the relay didn't buzz and the car started.

As it turned out the wire from the battery that held the 25 amp fuse was corroded at the end that connects to the battery. The corrosion had worked its way up the wire under the insulation. I assume that the corrosion had increased the resistance in that wire that fed the fuel injection relay. It still carried enough current to register the voltage on the meter but there evidently wasn't enough current to operate the relay.

The 7/940 cars don't have that heavier fused wire from the battery to the relay. They do however have several additional wires coming off of the positive post clamp. Perhaps one of those feeds the relay in the tray??

At any rate I would remove the positive clamp and the wires attached to it. Give the additional wires attached there a good look for evidence of corrosion as well as the possibility of the insulation hiding corrosion.
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Any twenty minute job is just a broken bolt away from a three day ordeal