What does the shift lever connect to that moves the linkage under the dashboard that could break?

Under the dashboard implies a column shift. This would mean a mechanical linkage. If so there is a connection on the steering column just outside the firewall in the engine compartment, a rod down to the frame and another rod to the transmission. At any one of these points there is a hard plastic or brass bushing. The rod may have come out of the bushing, the bushing worn or missing. The entire length of the shift rod should be visible and worn or broken point found.