Kira- Sounds like the ft shifter pod internals are not fully working. The Shimano twin lever shifters have little pawls that pivot on posts, a hair thin spring keeps the pawls against the cable spool's teeth. When the lube on these pawl posts gets old it gets sticky and the tiny springs can't keep the pawl against the teeth, hence no cable movements and no index engagement. Removing the plastic cover (watch out for those small screws don't get lost) and spraying with a cleaning solvent usually removes the sticky old lube, then relube after. Sometimes the pawls are so sticky that you might have to remove the "E" clip at the end of the post and remove the pawl totally to clean and lube.

We see this at work frequently. Some customers want new shifters (peace of mind) some let us do the servicing. We usually replace the cable as we will remove the shift pod from the bars to soak in out solvent tank. After soaking we Clean Streak the pod, flush with TriFlow spray and finish off with Phil oil and an air blast to drive the oil inside all. These shifters have a lot of tiny parts that can get lost on the floor very easily, so we try to not do too much take apart.

BTW if your LBS mechanic isn't willing to take 5 minutes to assess your problem and talk about the fix, at no cost, then you need to find another shop. We do this all the time. We don't discribe the repair process (as I have above) but we do explane the basic situation and path of service.