We have conducted a radio pulsar survey of 56 unidentified \gamma -ray sources from the 3rd EGRET catalog which are at intermediate Galactic latitudes ( 5 ^ { \circ } < |b| < 73 ^ { \circ } ) . For each source , four interleaved 35-minute pointings were made with the 13-beam , 1400-MHz multibeam receiver on the Parkes 64-m radio telescope . This covered the 95 % error box of each source at a limiting sensitivity of \sim 0.2 mJy to pulsed radio emission for periods P \gtrsim 10 ms and dispersion measures \lesssim 50 pc cm ^ { -3 } . Roughly half of the unidentified \gamma -ray sources at |b| > 5 ^ { \circ } with no proposed active galactic nucleus counterpart were covered in this survey . We detected nine isolated pulsars and four recycled binary pulsars , with three from each class being new . Timing observations suggest that only one of the pulsars has a spin-down luminosity which is even marginally consistent with the inferred luminosity of its coincident EGRET source . Our results suggest that population models , which include the Gould belt as a component , overestimate the number of isolated pulsars among the mid-latitude Galactic \gamma -ray sources and that it is unlikely that Gould belt pulsars make up the majority of these sources . However , the possibility of steep pulsar radio spectra and the confusion of terrestrial radio interference with long-period pulsars ( P \gtrsim 200 ms ) having very low dispersion measures ( \lesssim 10 pc cm ^ { -3 } , expected for sources at a distance of less than about 1 kpc ) prevent us from strongly ruling out this hypothesis . Our results also do not support the hypothesis that millisecond pulsars make up the majority of these sources . Non-pulsar source classes should therefore be further investigated as possible counterparts to the unidentified EGRET sources at intermediate Galactic latitudes .