It’s not to say a ground issue wouldn’t cause a fast blink, but it’s not the first place I’d look. Ground issues normally cause back feeding that would also give you other weird symptoms besides fast blinkers.
In spite of you being sure that all your lights work, fast blinkers would more likely indicate that a bulb is burned out on each side. What can trip you up is the bulb count for each function. There are probably at least two bulbs per side in the tail lights and both would function for running lights, turn signals, and brake lights in each lamp. (It’s a pretty common thing for GM passenger cars.) I’ve seen it mostly in my fleet mechanic days, but it’s not impossible for you to have had an innermost bulb burn out on each side while you’re looking at the ones still working assuming it’s normal.
Another thing I’ve seen many people miss is the front corner lights. They’re usually the little 194 bulbs. I’ve seen both of them burned simultaneously a thousand times too. They’re usually part of the turn signal circuits too. People never know they actually need to look for a bulb there because the primary turn signal bulb functions as a running too. They’ll alternate flashing with the ##57 bulbs.
Whether or not it’s a socket issue is a little tricky to address here depending on how accurate your assertion is that all your lights work. If they, in fact, do all work, then a corroded socket can’t be at play. At least not yet anyway. All of your bulbs working proves that point for you.