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@Mark, you have two very strong approaches provided above, and I am going to offer a 3rd.
You like the tabs (which I kind of do), and I am guessing, you have no issue knowing which string and fret you see on the page, and can get to it. I wonder, can you move to that note by note by note without looking at your hands? If you can, and you will eventually, that is the memory you are worried about kicking in.
I build playing without looking as a goal to every lesson. Now I cannot do what @jumpin’Jeff can do (yet), and while I can do what @MommaTAC does, i don’t, as it never sounds like the string playing to me. But when I can move through the strings and frets without seeing where my hands are going (even for 2 or so bars of the lesson), I know that my memory is working. If it is a piece I like, I work on it without looking at the page. Success? Sometimes, but Progress? Always.
There is never one way to build skill, memory, tonal recognition. By working at it, though, you are moving toward your “by ear” goal, and great job.