Adding 2nd receiver options

[Hall]

The only RG6 I have is 50' + lengths (with connectors on ends already), made up by either Dish or TW technicians. The short piece(s) of RG59 I had were actually the pieces that Dish includes with receivers.

 

[KKlare]

Rabbit ears are not the best for UHF, they are intended for lower frequencies like VHF. The loop, often given with or part of the RE does a better job. An amplified and/or multi-bowtie antenna does better still.
The only RG-59 around the house now has yellowed dielectric so that would discourage me. You can recognize the RG-6 with its foam dielectric and slightly large size core, which makes it stiffer. If it is loose inserting into the connector it is likely RG-59.
-Ken