I know Genies use a digital signal modulated on a VLF carrier, older GDO's were simple series optical switch's and could be jumped, but that is no longer possible for safety, if GDO's electronics does not see the correct signal it will not function.
Also I have found that strong AM broadcast radio stations in close proximity to the dwelling can render the system useless, I had a customer try three Genie GDO's and even had a factory tech come out 4 times but no one could figure it out, then the builder called me to meet with the Genie tech, I took a toner receiver (telephone) placed it next to the eye wire and out came the radio station that was less then 1200 feet from this house, went to my truck got a telephone RFI trap and put it on the terminals and the problem went away, Genie tech looked quite puzzled as they said they have never ran into this before.