B757 First Officer reported during cruise the aircraft experienced hydraulic system malfunction resulting in landing at an alternate airport.

Narrative

At cruise FL340; about 350nm to the east of the ZZZ on pacific track we noted a R HYD QTY EICAS caution. We pulled up the checklist and noted on the status page that the R HYD quantity was 0.60 and falling rapidly. We completed the checklist which drove us to turn off both the R ENG HYD and R ELEC HYD pumps. With the checklist complete; the CA attempted to contact Dispatch and Maintenance Control on ZZZ radio but they were unable to make the phone patch. The R HYD quantity got down to a low of 0.06 prior to turning off the pumps; and recovered and remained at 0.20 for the rest of the flight. The R HYD QTY checklist directs the crew to turn back on the associated HYD pumps prior to landing. However; both the Captain and I were concerned that with no fluid it could result in a hydraulic system pressure EICAS at low altitude and a go around to run the new checklist. After coasting in and contacting ZZZ1; CA was able to contact Maintenance Control on VHF. With their concurrence; we elected to run the right hydraulic system pressure checklist with the understanding that if we were to turn the pumps back on; there would be no fluid therefore no pressure. We [requested priority handling] and landed on Runway XXR at flaps 20. We requested the fire department follow us to the gate after noting that the brake temperatures peaked at a level of six.