Picked up a '65 Valiant 100

Mine does too. You could actually come right off the reverse fork with a lever coming through the floor. Put a boot around it. It would be located further left and back from the center of the transmission hump. You could actually put the lever under the dash and make it look factory. If you look at the thread where the guys are restoring Butch Leal's Duster, you'll see a good example of a stand alone reverse lever. I'd be really cool I think.
Do you have a link for that thread? I can't seem to find it.