"I have my kadet senior left over wings with barndoor ailerons on them and would like to build a fuse with a pusher engine in the back and a sq. alum. tube out the back and just put on the horiz stab and elev. no vert. fin/rudder

would it be a squirrly thing?"
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It won't be squirrelly at all, about 25 feet into the takeoff run. Then it will turn itself into junk at 26'.
YES, a vertical surface is needed, for the configuation specified.