After returning the turn signal switch to center, the turn signal "clicking" continues in fast, irrugualar clicks for several seconds. This also happens sometimes on startup. The turn signals and dash lights do NOT continue to flash in time with the clicking.
This is a common issue; typically the problem, is the contacts inside the turn signal lever assembly. Here is a DIY repair thread; on the issue and how to fix it,. Considering, how much disassembly required; I would just replace the turn signal assembly:
I had the exact same issue with the "clicking" continuing afterwards (with no lights flashing). Sometimes it would also click very quickly, and then it would randomly click even when I haven't turned on my turn signals.
Before replacing anything: try spraying electrical contact cleaner in the turn signal stalk. Move the turn signal stalk up and down several times.
I think mine just gets very dirty? Either way, this fixed my issue. The issue returned about 6 months later - repeat - and it hasn't happened again in over 8 months.