I believe the tail fin is just glued to the top of the fuselage on that pane. if wobbly it might be that the covering is the only thing holding it on and upright. that's always a weak spot. I can't count how many wobbly fins I've seen on planes of this design.
a good fix, is to cut the covering at the fuse/fin joint and add a small basswood vertical spar along the entire trailing edge of the fin that extends down along the end of the fuselage. this will strengthen the attachment and alignment between fuselage and fin without adding much weight. then, re-hinge the rudder off that spar. I do that to all my vert. stab mountings. you'll have to readjust your rudder center afterwards, but the should be plenty of adjustment in the linkage to compensate for that spar. make the spar 1/4 inch by what ever thickness the end of the fuselage is and use epoxy to re-glue the new fin assembly to the fuselage.
and as mentioned,....Never,....run an engine without a prop mounted. you are lucky you still have an engine !.
Last edited by r ward; 08-05-2018 at 08:32 AM.