The FT-60 manual says the battery pack is a NiMH pack ("FNB-83 (7.2 V, 1400 mAh)"); so, as we usually use 1.2V as the nominal voltage of a single NiMH cell, a pack of 6 cells in series.
You'd usually make sure not to discharge a NiMH below 1.0 – 1.1 V; going deeper can damage the cell. So, the minimal voltage for a pack of 6 in series would be 6.0 – 6.6V.
I'd very much expect your FT-60 (or the battery pack itself) to have a protection circuit that simply doesn't allow to deep-discharge your pack, i.e. your handset will very likely simply stop working as soon as the battery pack voltage drops to 6.0 V.
Regarding your 9 V: For charging, you have to apply a voltage slightly higher than what the batteries nominally supply (charging efficiency is chemically never 100%), so, when observing the voltage across the battery pack during charging, it should be > 7.2 V, and a bit lower, but still > 7.2 V for a short duration thereafter, but the voltage will drop very quickly as soon as you start drawing current from the battery, and then stay relatively constant (or rather: drop relatively slowly) between 7.2 V and 6.0 V.
This is all a bit approximate, since it depends on the making of the individual cells and the amount of current drawn, but generally, NiMH cells have a relatively flat "discharge curve" (i.e. after drawing an amount of mAh, how much voltage can be measured across the battery?).
The takeaway is that you can, optimally, just use the batteries until the FT-60 reports them "flat", not shorter, not longer. NiMH don't (as significantly) suffer from the "memory effect" that NiCd exposed, so there's nothing to be lost when you really just charge your batteries overnight, and then use them as long as they work.
Personally, with the moderate current drawn by the handset, and the voltage, I would've designed the device to work with LiIon batteries – these could pack more energy into the same size and weight than NiMH – and you'd have a longer talk time. However, LiIon is a bit harder to make safe, so that might have come out a bit more expensive. Then again, those batteries are what powers smartphones these days, so the economics of scale would probably have made them cheap.