IIRC, we had a few do that at the dealership when I was an
apprentice.  IIRC, it was a broken reverse strut in the
trans causing the problem in that year model.  There was an
update to correct it but, I just don't have the recall to
come up with the details.

Lugnut

Lugnut

The park mechanism is operated by a dedicated cable that that enters the
bottom of the tailhousing, if the cable or the shifter is out of adjustment
the park mechanism can engage while the car is moving
Both the column and console shifters have a mechanism that moves the cable
only when shifted to the Park position, if the shifter is worn it might not
fully retract the cable when shifted out of Park.
The cable adjustment is outlined in the service manual.

If the second gear band or reverse band applies for some hydraulic problem
this can occur. I have seen worn front pump to front drum sealing rings
cause the second gear band to stay partially engaged in 3rd, any way it has
to come out and apart, did this happen after the valve body was done? As
mentioned the reverse apply strut can cause this also, anything  causing 2
opposed units to be on at the same time.

My first suspect would be the park lock mechanism. The '65 torqueflite
is a one-year-wonder in that regard. It uses separate cables for gear
selection and park engagement because the transmissions were still
pushbutton operated in '64, but for 65 the cables are both operated by a
shift lever instead of pushbuttons. It requires accurate adjustment of
the park lock cable in sync with the gear select cable to be sure it
works right. Heck, the park lock cable could be broken or disconnected-
does it lock the wheels like it should in PARK?

Since you say it locks in *first* gear, that kinda rules out the bands
as a problem- if the reverse band applies in first gear, you
get....FIRST GEAR (the reverse band engages when you select manual first
anyway- that's the only difference between manual first and automatic
first.) If the second-gear band engages, then you get... SECOND gear,
not a lockup. Lockup would require *both* bands engaging, or else either
band AND the direct (front) clutch engaging at the same time. IOW, two
things have to go wrong at the same time to force a lockup when its in
first gear.

All that said, I'm always very suspicious of shift kits in '65 and
earlier Torqueflites. There are enough hydraulic differences in the 65
and older transmissions that some (not all!) shift kits can do really
stupid things if used in them.