Panic at the ISCO: time-varying double-peaked broad lines from evolving accretion disks are common amongst optically variable AGN

About 3-10\% of Type I active galactic nuclei (AGN) have double-peaked broad Balmer lines in their optical spectra originating from the motion of gas in their accretion disk. Double-peaked profiles arise not only in AGN, but occasionally appear during optical flares from tidal disruption events and changing-state AGN. In this paper we identify 250 double-peaked emitters (DPEs) amongst a parent sample of optically variable broad-line AGN in the Zwicky Transient Facility (ZTF) survey, corresponding to a DPE fraction of 19\%. We model spectra of the broad H$\alpha$ emission line regions and provide a catalog of the fitted accretion disk properties for the 250 DPEs. Analysis of power spectra derived from the 5 year ZTF light curves finds that DPE light curves have similar amplitudes and power law indices to other broad-line AGN. Follow-up spectroscopy of 12 DPEs reveals that $\sim$50\% display significant changes in the relative strengths of their red and blue peaks over long $10-20$ year timescales, indicating that broad-line profile changes arising from spiral arm or hotspot rotation are common amongst optically variable DPEs. Analysis of the accretion disk parameters derived from spectroscopic modeling provides evidence that DPEs are not in a special accretion state, but are simply normal broad-line AGN viewed under the right conditions for the accretion disk to be easily visible. We include inspiraling SMBH binary candidate SDSSJ1430+2303 in our analysis, and discuss how its photometric and spectroscopic variability is consistent with the disk-emitting AGN population in ZTF.