We investigate whether gamma-ray pulsars viewed at a large angle to the neu
tron star magnetic pole could contribute to the new population of Galactic
unidentified EGRET sources associated with the Gould Belt. The faint, soft
nature of these sources is distinctly different from both the properties of
unidentified EGRET sources along the Galactic plane and the properties of
the known gamma-ray pulsars. We explore the possibility, within the polar c
ap model, that some of these sources are emission from pulsars seen at line
s of sight that miss both the bright gamma-ray cone beams and the radio bea
m. The off-beam gamma rays come from high-altitude curvature emission of pr
imary particles, are radiated over a large solid angle and have a much soft
er spectrum than that of the main beams. We estimate that the relative dete
ctability of such off-beam emission is about a factor of 4-5 higher than th
at of the on-beam emission. At least some of the radio-quiet Gould Belt sou
rces detected by EGRET could therefore be such off-beam gamma-ray pulsars.
The Gamma-ray Large Area Space Telescope should be able to detect pulsation
s in most of these sources.