When I saw this ballast, I thought that it might work well for 2 F13T5s wired in preheat (one red wire for each lamp). Would this work? I have gotten a 1 lamp F20 TS ballast to rapid start an F13T5 and it worked, so I know the OCV is OK. Will this really work?

The F20T12 is a 0.37A lamp, the F13T5 0.16A lamp. Because the OCV is in the 200V range, the current will still be rather high, beside the higher arc voltage.
So yes, it will light, but it will also toast the lamp after some time.

The F20T12 is a 0.37A lamp, the F13T5 0.16A lamp. Because the OCV is in the 200V range, the current will still be rather high, beside the higher arc voltage.
So yes, it will light, but it will also toast the lamp after some time.

What about 2 lamps in parallel, one on each red wire?

Only one will light and take all the current.
Depend on the internal circuit, either the two red wires are essentially shorted together (with just low voltage winding between them, so for the arc essentially a short circuit) or only one of them is powered (and the other is used just for starting to warm up the corresponding filament).
You would need some autoteransformer or so to split the current equally even when the voltages differ. But that would mean essentially another ballast in the circuit, so having two proper ballast would do at the end a better job...