@lowrider57 Pictures are worth a thousand words......
Especially this one.....
https://ibb.co/qpQnYf5
Your service entrance drop is a cable. It is not a conduit with wire installed in it as I imagined.
It appears to me rain water is entering between the outer sheath of the service cable and the weather proof strain relief connector on the top of the meter socket. My guess is the rubber bushing, (or possibly, depending on the age of the connector, Oakum Packing Material), that is supposed to seal the service cable and the metal connector from allowing water from entering the meter socket is shot, deteriorated, allowing water to enter.
A band aid that may stop/help from rain water from entering the connector, therein the top of the surface mounted meter socket is to apply a good quality pure silicone caulking around the service cable and the weather proof strain relief connector.
Clean the cable with a dampened dish soap and water washcloth at least a couple of inches above the top of the connector and the entire top of the screw down cap/nut of the connector. Remove any loose debris that may be laying between the cable and the inside of the connector. Rinse off the soap with a slightly water dampened clean washcloth. Repeat as necessary to remove all dirt and soap. Repeat process if needed to get all surfaces clean. Allow to completely dry several hours. Surface areas must be 100% dry.
Apply the pure silicone caulk around the cable where it enters the connector throat, opening. Make sure you force, inject, as much silicone into the top of the connector between the cable and the connector as possible.
Finish off forming the silicone product using your finger. You want the silicone caulk to cover the top nut of the connector so the water will shed down the side of the connector.
Next using your finger slightly form, taper, the silicone caulk up all around the cable. Do not leave any globed pockets for water to puddle. You want the finish product to look like cone.
(To stop the silicone from sticking to your finger, as you form it, slightly moisten the tip of your finger with water as you form the silicon.)
Jim.