DP Twin or DPP Twin are equally compatible with 612. Make sure it's not an early Twin; those are not DP (though that can actually be used, with dual-run coax). Need to use a high-freq. splitter at the 612 (to connect both sat tuner inputs) if a single coax run to the dish. Most likely cause for only being able to peak one sat position at a go is mis-setting of skew. That's the circular bolted interface on the 500 mount. There's probably an instructional somewhere that tells where to set for your latitude, or someone here can probably give a quick explainer. I just haven't done it in quite awhile. A bent dish pan can also cause this kind of issue.
