1965 Dodge Dart GT convertible with 318 and 727 Transmission, linkage or cables do not work.

there might be an easy fix.
In your case it seems that your shifter and your manual control valve are not synced.
But before we get started, e gotta prove that your manual valve is working correctly. To do that; get the rear wheels off the ground, and disconnect the linkage off the shift lever down at the trans. Put the trans in park to lock the driveshaft, so that you know where Park is. Ok now start the engine and make sure all the gear positions work. Do not shift into Park if the driveshaft is spinning. If you find all gears, shut the engine off, and then we can proceed.
Step 1
disconnect the shift linkage off the shift lever, down at the trans. then put the trans in "Drive". It is very important that the trans be in Drive and NOT in Neutral. Next put the shifter also in drive. Next adjust the linkage/cable to drop into the lever. Lock the slack adjuster.
Step 2
Next, disconnect the linkage from the lever again. Put the trans in park, making sure park is engaged,all the way, locking the driveshaft; then put the shifter also in Park.
Now comes the Sync check.
attempt to drop the linkage back onto the shift lever. If the hole is out of alignment, you have the wrong ratio trans shift lever. So,
Step 3
figure out how to put it back into sync by moving the hole closer to the VB or further away, as the case may be, and then ,either; 1) go to the junkyard and get what you need, or 2) modify yours.

Those levers come in 2 or 3 ratios and various bends, for various bodies, and their designated linkages.. You can bet that your Early Dart never came with a 727, so if your 727 has a shiftlever on it from a Polara or something, it may not work.
Easy Fix
Happy HotRodding