That is normal behavior for a non functioning antenna. It takes very little energy and antenna to receive, but much more antenna and power to transmit.
I'd recommend getting a fiberglass deck level antenna as a backup antenna for your vhf, and fix your mast antenna. I'd bet you'd get a good response to radio checks when you connect the fiberglass deck antenna to the vhf. The problem with the mast antenna sounds like a corroded cable, connections, or antenna.
I don't know anything about splitting an antenna between an FM and vhf radio, but that may be an issue too.
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