I suspected the problem was the timer behind the panel and/or the timer dial in front (which was not working correctly and didn't click/stop at most of the stops). Kay, the very helpful customer service person, showed me online the schematic for my dryer (Maytag and Model No.) so I could identify and pinpoint the exact parts I needed. The timer dial was deceptive since it is 3 connected parts, not just one piece. Then Kay pointed out that there was also a specific and helpful short video on how to replace the timer dial.
The pricing was excellent compared to other vendors, the parts were received quickly, and I replaced both timer and the dial on the 19-year-old but in good shape dryer (the igniter was replaced in 2011). Replacing the timer is tedious with 12 connections and no mixups allowed; replacing the timer dial is easy. Now the dryer works great and I am keeping the old-timer as a backup (though old, it may be ok). I saw on websites that timers frequently fail, so with a new timer installed it is likely good for the duration of the dryer.
Using AppliancePartsPros saved me approximately $200 (parts and labor) over using an appliance repair service. I recommend them highly.