just brought home a 1965 f350 with the 240 engine and 4 speed transmission. trans has 4 forward gears and with second shifter can be shifted into reverse and shifted through all four gears. truck was originally purchased by the Chicago and Northwestern railroad. looked all over internet but haven't seen this combo yet.

 

Welcome to the forum. Your question would probably be best answered if posted on the forum section of FTE that concentrated on the 1965 year vehicles. Detail pictures of the auxiliary transmission or auxiliary shifting device would be helpful in IDing what you have. Well stated questions usually get good answers.