Are you sure? I don't think the red LEDs on the pickup board are visible without first removing the alternator rotor and stator (I may be wrong about that though, it's been a while since I looked in there).
Those little LEDs are a good diagnostic tool so it's definitely worth checking them.
It's a simple job to get in there and doesn't disturb ignition timing. Red will have supplied a puller to remove the alternator rotor. Remember that the big nut holding the rotor on has a left-hand thread. Remove the nut, attach the puller with the 3 bolts, tighten the centre bolt against the end of the crank and the rotor should pop off its taper easily. Don't lose the Woodruff key. Once the rotor is off, the stator winding is held on by 3 socket-head screws, but first remove the little wiring loom retainer at the bottom so you have enough slack in the wires to pull the stator winding off over the end of the crank.
It's safe to crank the engine with the alternator stator dangling from its wire loom. If you see the LEDs flashing when the engine is cranked, all is well and you can put it back together. If the LEDs remain dark, then you're almost there with a diagnosis.