GA pilot reported an electrical failure resulting in the destination tower using light signals for clearance to land. After one missed approach due to no light signals; the next approach was successful.

Narrative

Flying back from ZZZ; usual route is tank farm to ZZZ1 per school policy. Light rain began and crackling on the headsets near tank farm. We descended circling over the tank farm from 3;500 MSL to 2;000 MSL and reduced our speed to see if it improved. No change. We attempted to contact ZZZ1 with our position and got only crackling. Weather info was recorded via foreflight. We squawked 7600 and ident; then proceeded inbound for a left base Runway XX the usual instruction in this weather condition. Watched ADS-B and saw no traffic; proceeded with caution. Requested light signals and rocked our wings. Ident again. First pass was a go-around because no light signals were received. Radioed Tower on climb requesting light signals; mentioning we had no radio reception. Made left traffic. No traffic in sight or on ADS-B. Light signals received on second attempt at final Runway XX. Solid green. Landed; turn off Taxiway 1. Flashing green. After-landing configuration; then proceeded the usual taxi route Taxiway 2; 3; 4 to FBO Ramp.