Have both the converter and battery checked. The converter should have capacity to run the furnace without the lights dimming and the radio cutting out. The battery may be going bad also and is constantly drawing a charge. In cold temperatures that kind of problem can be more possible. Take the battery to Advanced Auto, Sears or a battery shop and have them load test it. Simply testing with a volt meter may not tell you anything.
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My Great Wife Joyce
2018 Jayco Jay Flight 21QB
Formerly owned 1705T and 2310H
2012 F150 4X4 SuperCrew EcoBoost w/Leer Cap
Reese WD Strait-Line Hitch
Amateur Radio K3EXU
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