Easy first step for turn signals is to use a battery brush on the sockets and a little grease. Of course, all seven, I think, grounds in the engine compartment need to be cleaned and greased.
See, I'm a jerk and left both my multi-meter and power-probe at work, an hour away, last night. Now I get to spend all weekend on my car with the mystery electrical issue, with no diagnostic tools. But thanks Wolf, I do believe I have a tube of di-electric grease, a wire brush, and an angle grinder. At least I can rule out a silly ground issue.
In fact, maybe I'll go a bit wild with it. I can run a big fat ground from where I grounded the battery to the chassis, to the block and to the head. Then I can collect those (4 or 5, I think) little grounds all around the battery tray, and thermostat housing and run them right to the big lug I installed. I think there is one last little ground over by the FR headlamp/PS pump, I'd probably run that little guy over there too. Then I can check all of my engine grounds in one spot!