Starter not operating when installed but operating when bench tested is typical for tractor having poor battery cables or poor battery cable connections
Brand new battery and brand new negative cable. I tested them for continuity just to be sure. When I tried jumping the starter from my truck, the positive on the starter, alternator and battery all measured at 14.5 volts.
Brand new battery really means nothing. I've had multiple bad, brand new batteries before. Reading static voltage on a battery also tells you nothing. Measure that voltage as you turn the starter over. Load testing things is the only way to know you have a good power source and good connections.
So on a bench test the starter spins fine. Install said starter and short the terminals and the starter won't spin. That my friend is a bad battery or a bad connection somewhere between the battery and the starter. Or.....the starter is intermittent. The only reason we harp on these things is because we've seen it on this forum 100 times.