Radio shuts off and on repeatedly

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Just bought a very clean SL550 with only 10,000 miles. After 4 days the right tail light (not brake light) went out then the radio started turning on and off then on again...every 45 seconds or so. The dealer told me that BOTH keys fobs had dead batteries in them and the new batteries are still on order, but Im beginning to wonder now if the doors not locking and unlocking is really a battery issue or more electronic stuff. Help with radio!!