Identification of gamma-ray-emitting Galactic sources is a long-standing problem in astrophysics. One such source, 1AGL J2022+4032, coincident with the interior of the radio shell of the supernova remnant Gamma Cygni (SNR G78.2+2.1) in the Cygnus Region, has recently been identified by Fermi as a gamma-ray pulsar, LAT PSR J2021+4026. We present long-term observations of 1AGL J2022+4032 with the AGILE gamma-ray telescope, measuring its flux and light curve. We compare the light curve of 1AGL J2022+4032 with that of 1AGL J2021+3652 (PSR J2021+3651), showing that the flux variability of 1AGL J2022+4032 appears to be greater than the level predicted from statistical and systematic effects and producing detailed simulations to estimate the probability of the apparent observed variability. We evaluate the possibility that the gamma-ray emission may be due to the superposition of two or more point sources, some of which may be variable, considering a number of possible counterparts. We consider the possibility of a nearby X-ray quiet microquasar contributing to the flux of 1AGL J2022+4032 to be more likely than the hypotheses of a background blazar or intrinsic gamma-ray variabilty of LAT PSR J2021+4026.