SO, first, a video that explains quickly all of Granpa Semi (Semi Seriff). Now if you know EVERYTHING about Granpa Semi, then continue down!
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NOW that we're on the same page, I think Granpa Semi is what inspired Gerson's writting, theme and role on Chapter 4.

All of the darkners in Deltarune are remixes of ides and characters seen in Undertale, SPECIALLY the secret bosses (before you call it BS, Undertale was a test game for Deltarune, not helped by what seems to be Reverse Undertale theory being proven with what we've seen).

Jevil is an evil Sans, possibly a mix with Chara due to how disconnected from the story (it's a bit of a mess, maybe we'll see it more clearly in the future)

Spamton is OBVIOUSLY Mad Mew Mew (formely Mad Dummy) and Mettaton combined, there's so many pararells it makes my head spin.

ERAM seems to be a mix between Flowey with how they act and seems to be an Amalgam? Saying this because of not only their link to FRIEND (__) and the Knight, but also because it resembles an Amalgam sprite.

The Roaring Knight is a mix of Asriel Dreemurr with their presence in general and Undyne's Knight role throughout Waterfall hunting us down.

Gerson for me was a mix of Undyne (I mean, he was HER mentor in Undertale before Asgore took her in) and Sans, with how he is a comedic relief character that's ever present and hides their true power and knowledge until their fights... But something felt off.

With the little knowledge of what originally was planned for Granpa Semi, I think now that not only many of his traits were passed on sans, but ALSO Gerson. While in Undertale, Sans took most of the traits Semi had, Gerson seemed to amplify what was originally planned for him, plot twists and all, for it seems Semi knew very too well about the color attacks and expanded on Sans blue monologue.

Gerson in Deltarune was WHAT was originally planned for him in Undertale, he even is ""Clumsy"" (but this is just guessing from the youtuber from above, I think it makes sense tho because... I'll get to that soon). Even Semi's name is a PUN, his name is not a font perse, but a font type, Semi Serif... Semi SHERIFF, thus why he owned a farm, and knowing the Royal Guard and all, he might've been the original Head Soldier of the Royal Guard before Undyne, something Gerson would take in the final release, which may be one of the coolest development fun facts if it ever got confirmed.

...
SO, remember how Gaster sees the eggs like ISSUES? Well, not only it's also a PUN since Eggs can be considered "Issues" as in OFFSPRING (Jokes run in the skeleton family!), but also may tie Semi to Gaster because BOTH went through the same thing, but while Gaster managed to somewhat get out, Semi got trapped and forgotten in the game.

DAMN I may go as far as Semi being responsible for the incident at the core that Gaster went through since both got the same treatment, both were forgotten and their roles were dispersed through Undertale, both become gooey messes in the code. The incident was INDEED an incident, one that could've been avoided if Semi had taken things more seriously...

But HEY, that's just aaaaaaaaaaa Head Canon, mixed with my own theories and such, you can think of Semi the way you want! For me? He's the Gerson we never got, and I'm glad that after so long, he's finally remembered!

Everyone rejoice!