Thanks, Loren. Oddly enough, on my laptop it's been very hard to find definitions (as I mentioned earlier, I'd been herded without compromise toward "digital", "detail", and the like), whereas on my smartphone (is that a dated term now?), sticking to the topic
I want and getting the pertinent definitions has been far, far easier. Weird. Anyway, as you've astutely guessed, "dital" refers to fingerly operation, and its root is attributed to the Italian "dito", or finger. "Dital" is indeed a term much like "pedal", and it is potentially just as general-purpose, the difference being that the word has fallen out of whatever use it had and now only lives on tenuously in obscure, geekworthy contexts such as a particular harp mechanism of the past, and novelty instruments such as Edward Light's "dital harp" (my correspondent diplomatically referred to Light as "bored and creative". Be that as it may, Light's instruments can command multiple thousands today. Investors take note).
Nowadays, rather than "dital" we would be more apt to say "toggle", or the like.
So since you're all dying to know, here's what I've gathered so far as regards
harps proper (this will be in
very general terms and no doubt there will be some errors in the fine points): The dital mechanism is a finger-operated variant of the single-action pedal mechanism, "single" meaning it only works one way, sharping the note; double action can sharpen
and flatten, a logical development and the one we see now in current concert pedal harps. If ditals were used for double action I'm as yet unaware of it, but I wouldn't rule it out. What a harp dital mechanism does, then, is sharpen (or possibly also flatten, depending) a particular note across all its octaves in one go - a partial capo, you could say - whereas like sharping levers, Light's mechanisms were individuals, one each per string. Both systems were technically very different, too. Also, harp ditals locked into place. So far I don't know whether Light's buttons had the same capacity, but given that he (like Egan) marketed his instruments to privilege - in this case cultured demoiselles of the upper crust - one assumes Light wouldn't have cut such corners. Back to standing harps, here's a pic of one solution to the goal:

This is a Browne & Buckwell harp, made special in the 1920s for the famous harp professional Mildred Dilling, as I understand; if no one else is still making harps with ditals today, then this was possibly the last of its kind, and probably a revived instrument even that far back. Its form echoes one that Egan often worked with. Here the ditals are the upright thingies you see atop the neck; flip one down and you activate the mechanism, the bulk of which is hidden away inside the neck (my correspondent called it "a task for watchmakers"). Next is an actual Egan harp (and there's that bulbous-headed form again):

As you can see, in this case the ditals are on the post. I'm not 100% clear on whether that was his usual way, but I've seen it on other models of his as well (and up to now wondered what such intrusions were doing there).
While rather spiffy and convenient in its way, the dital system never sustained widespread acceptance on these smaller harps, and the reasons were several: A) With ditals you were limited to the unvaryingly foursquare layout of a note sharpened all across its octaves, whereas individual levers (which I now learn had predated the dital system, which makes sense) could do the same AND you could get wild and do
scordatura as well. The dital system couldn't; you would have to manually retune for the purpose. B) The dital mechanism was comparatively clunky and slower in response than the more agile levers when all you might need was a passing accidental; either way, you had to fumble with something. C) It was noisy. D) It was heavy; a smallish harp with a full array of dital mechanisms could weigh as much as 40 lbs, which made the much-touted "portable" aspect open to debate. E) It was very costly: at £30 it was the same price, in that period, as a small rural cottage or a few years' servant's wages, and times were hard and getting harder. Further, I personally would add an F): Let's face it, harp ditals are frankly unattractive to the eye - jutty, odd, and indiscreet. And from an Everyman's standpoint, Egan's post-mounded ditals made the custom of carrying the harp by its curved post a tricky proposition. My correspondent said Egan's genius was in making the mechanism work reliably on such a small instrument.
The technological reversal to individual levers was in the end a sensible choice, I think. Dilling herself went back to them on her smaller harps. Some portable harps don't even have sharping levers these days; a loose comparison would be keyless vs. keyed flutes.
So now you (and I) know! And you can use "dital" with impunity and all confidence (not to mention authority

) the next time you play Scrabble.

Oh, and I still don't yet know how "dital" is pronounced in English. Merriam Webster takes no stand but throws up its hands and suggests "deetle", "dittle", and "dytle" all. Take your pick. I keep saying "dytle", so I think I'll stick with that.