A 727 of that vintage that came from a light duty car or pickup would more than likely be a "lock up torque converter" version. That is not a good thing as far as durability when used in a relatively heavy vehicle with much horsepower. That was an early attempt at squeezing the last ounce of fuel out of a mile forced upon the manufacturers by the feds.
The durability of the lockup torque converters and their paired transmissions is dismal. That does not reflect upon the lockup systems used in more evolved versions of the 727 family today. Ya can't compare the two!
So let's try and id exactly which tranny ya got. On the pan rail just below the shift lever you should find a string of stamped number and letters. Inna true chrysler app, that number will most likely be the original donor vehicle vin, if it's a service part tranny, then it "might" have had the vin re-stamped into the case. No matter...see if ya can read and then post that string of numbers exactly as you see it. A nice phot would be even better!
Pic I've attached shows the location. This 727 is a very early unit.
Ihc versions of the tf 727 (code t-407) normally have the service part number or the oem part number stamped in the pan rail, not the vin.
Since it's not currently mobile in the true sense of the word, the only other way to determine which version ya have is tear it down.
A "lockup" torque converter has a hydraulic-apply clutch inside with a friction material face. Under light cruise load/rpm, the valve body will tell the tc clutch to "apply"...in some cases if the tranny and tc are in good shape, you can feel this happen, but it's not near as noticeable as when a four speed automatic goes into "overdrive".
Sorry, I forgot to answer your question! No it's not supposed to act as you describe. The lockup action and overall performance of the transmission should be just like any other oem autotrans. The lockup action near imperceptible when it occurs.
