The reality is within the industrial engine powered realm, there really are no true manual, geared, shift on the fly transmissions available.
sadly true.. but there WAS one.. unfortunately it's next to impossible to find out who made it.
so the only chance to get a good glimpse of one is to buy
a realy expensive kids car
(the Lorinser SL 350, the Porsche 911 Junior ...)
and take it apart
to find this:
manual 3+R transmission good for ~5horses to be shifted on the go.
(that one's IIRC a GX120 from a 500SL Mercedes, there's a similar one with a G160 (not GX) in the Porsche junior)
and the Lorinser IIRC had a Briggs flattie (3horse?) with a different gearbox.
some such cars came with a a mower transxle alright,
but few had a true shiftable gearbox.
the ones that had a clutch pedal were all shiftable while driving AFAIK.
'sid