I can see why you're disappointed! There are a couple of workarounds for the synching issue, but it would be good for Cyberlink to know about the patch problem and that PD13 should allow audio tracks in the mix.
For your syncing issue, the simplest approach would be to place your audio-only track by itself in the timeline and just produce it as a video clip, as a .wmv, .mp4, etc.. The video will be blank of course, but when you place it in the timeline it won't disable the Sync by Audio button. It's an extra step, but it should only take about 20 seconds.
Another option is to use the multicam designer (MCD), which will let you sync up to 4 videos clips AND an audio-only track. I know you felt like that feature was a separate entity, but it actually integrates very well with the main editor even though some of the functions aren't immediately apparent.
I'd suggest that you import just one video clip along with the audio clip, then sync by audio (assuming they both have the same music track on them) then note the offset of the clips. This way PD13 has done the tedious work for you and it might be easiest to just make note of the offset, cancel the MCD and place those 2 tracks on the main timeline with the same offset. You'd probably want to do that
after you've synced the video clips in the main timeline.
You can actually use the MCD to create your entire video, especially if you have no more than 4 concurrent video clips at any one time. It's actually a very powerful tool that came out in PD12, and you may want to look at some of these
tutorials to get a deeper understanding of how it works and whether it can help with your music video.
Hopefully one of these will be a good fit for this project!
YouTube/optodata
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