The flywheel needs to be removed to access the alternator.

But where does the wire that broke off terminate from the engine? My guess is that the wire is fine from the flywheel down to where ever it broke off to what I see on the outside lying near the starter.

What does that wire do? Is it needed since it seems it might have been broken for a while.

Thanks

Could you tell us the brand and model number of the machine this engine is in?
And I don't think you mentioned the color of the wire that is broken.

Generally on a 28 series Briggs, alternator wiring is done one of two ways.

If machine has electric start but no headlights, a single wire will come from the engine and connect to the machine harness by various connectors (spade, QC, etc.). Provides rectified DC for battery charging.

If machine has lights, there will be two wires together coming from engine ending is a single, two pole connector. One of the wires will have a diode in series (under heat shrink) and provides DC for battery charging. Other wire provides AC for lighting purposes.

If you have a single broken wire, it probably goes to the mating connector which in turn connects to the connector coming from the engine.