Do not put any dielectric grease on anything until you have found the broken wire or bad connection . Dielectric grease is an insulator and does not conduct electricity. It's primary purpose is to prevent moisture intrusion into electrical connections and help reduce corrosion.
Pins and contacts can be cleaned with electrical parts clearer that you can get at the auto parts stores. Toothbrushes and Q-tips can be used as needed to get to difficult to reach places.
Are you tilting the EEC relay when you move the computer? If so check the relay socket for moisture and damage. Look for signs of overheating on the socket and wires. Swap the EEC relay if you have a spare one handy.
I did the wiggle test on the relay and it did not seem to have any effect.
I cleaned the EEC pins and it seems to have all but cleared up the issue. It does slightly miss when I "vigorously" move eec around. I will clean it better when I have more light! I'm still worried that maybe something is wrong with the connector. The pins on the eec all appear intact.