Parking Brake Not Effective

Pulling on the parking/hand brake on the '65 Valiant Signet convertible does not apply the parking brake. The handle will slide out 1 3/4" and then comes to an abrupt stop. Looking underneath at the cables while I pull on the handle, I can see the main cable from the handle is free but the cables entering the brake drums are stuck.

I already tried squirting some penetrating oil into the two rear cables, but that rubbery seal around the cable makes it difficult. After the oil, I pulled on the handle time and time again with no change/improvement. Is there another trick out there I haven't thought of yet? Thank you.

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