Hi Drew,
Happy New Year. When in doubt, yes, you are right, start with a simple piece...not that one. It has too much going on. In YTube, there are many SLOW, very simple "backing tracks" that will show you the chord change a millisecond before the change. You can even look up some arpeggio backing tracks that have diagrams as you play- this can be very useful. I would find one of those- really slow, ideally just one other instrument like a slow piano track in E. I would also start only using one finger on the top E string for the first few minutes- just to get the feel for it- almost like playing base.
I just checked out that website and it's a great suggestion. Funny- it uses a piano- simple, slow and easy to track changes. Also, turn off all effects if you are playing electric. You are going for pure tone- not distractions whatsoever- forget that other song...for now.
TOP TIP: Print out a HUGE copy of the fretboard on legal paper. Find one that has all the notes for each fret- B&W is best. Then circle and/or color code each of the root notes for each chord change (use different colors for each e.g., I Blue IV Green V Red.) Not all the notes in the chord- just focus on the root note for now. This makes it soo much easier to see and hear what is going on. You can hunt down the other notes but as long as you find your way to the root note at or around the change, you will be playing IN HARMONY- now that is really playing (many people play scales but have no concept of harmony- it just sounds better- you can wonder off from time to time, but always come back.)
So IMO, the trick is that you really have to SEE, HEAR and FEEL what is going on. Writing it out also helps reinforce things. Once you practice one easy piece for about an hour or so, close your eyes and FEEL it- you'll know when this happens.
I would also echo the others and suggest you use that website to practice often (I will too.) Also, at least hum the chords- it you cant sing it (at least in your head), you can't play it. Pick one thing and master it before morning on to the next. I can play about 100 songs- maybe more...anything on YTube I can jump into and sound ok, but I only pay a few well. Those are the ones I am most proud of. Eventually pay attention to your strumming pattern, feel, etc. One last tip- don't forget to enjoy---this is supposed to be fun! (;