You should have EITHER the green or the brown connected. The green should go to coil negative and to the tach ONLY. If it was grounded to the firewall, that's no good.
If that green lead was connected to the coil and the firewall, I bet the coil(s) is(are) now damaged from excessive current.
You see, the coil gets power from the ignition switch. The ground on the coil goes to the ecm. The ecm switches the ground on/off as needed to make a spark. I'm willing to bet that if the green wire was grounded, the wire inside is burned and making a very slight connection causing the buzzing with the key on. Basically, your coil is "always on" before the engine is running. I'm surprised it can make a good enough spark, but if the green wire is now high resistance from being cooked (probably cooked while you were originally trying to get the engine started after the R&R) then the drop in primary voltage is probably still enough to get mostly reliable ignition. But... The coil is probably still seeing excessive current and overheating.
I say keep the tach completely disconnected for now and go drive some. See if it quits again.. Also, keep your spare coil and the tools to swap in the car with you for now. I bet that coil is on its last legs.