Apologies in advance, this is going to be a long post, but after many apparent mistakes here is my official typing. Heads up I could not really type these charcters until I see them interacting with Spongebob, so this post will mention him a lot (Karen being the exception).
Spongebob: ESFJ
Fe: A tidal wave of emotions ALL the time.
Si: Instead of reasoning he always searches back to what he has learned before.
Ne: thinks of a million ways thigs can either go right or wrong.
Ti: Rarely uses unquestioning logic in making decisions.
Patrick: ESTP
Se: What he first notices in every episode is his physical environment (ironically he is not very observant in picking up physical cues).
Ti: Uses creative construction combined with his Se to do some real crazy shit.
Fe: More in tuned with social norms than I realized, also is open about needing affection.
Ni: His underlying instinct is shown in many episodes that he blatantly ignores because of the false conclusions he bases off of physical evidence and a half baked attempt at logic.
Squidward: ISTJ
Si: Has always preferred the traditional method of things.
Te: Defys every little idea Spongebob comes up with by stating rock solid reasoning.
Fi: He likes his personal feelings to himself, but sometimes he needs Spongebob to grow as a squid.
Ne: Literally 10x worse than when Spongebob goes on an Ne attack.
Sandy: ISTP
Ti: A scientist who always responds to Spongebob's ideas with ideas with rational fine tuning.
Se: Adrenaline junkie, body builder, really knows her body.
Ni: Very spot on when she tries to figure out what the hell Sppongebob has done to mess up this time.
Fe: Very friendly, but never outspoken when it comes to her personal feelings.
Eugene Krabs: ESTJ
Te: If the greed can be taken away foe a minute, he is a pretty sensible crab who doesn't like to take any of Spongebob's crap.
Si: Literally everything surrounding him is memorabilia, and he always goes to what he knows when he tries to attract customers.
Ne: The episodes are a lot funnier when his Ne kicks in, coming up with some unimaginable stuff to improve business.
Fi: Never talks about his personal feelings at all (usually it's just Spongebob who picks up on this).
Plankton: INTP
Ti: His logic assists him in creating effective methods to get the formula (sadly he's not very gifted in planning ahead), hates unnecessary emotions a.k.a Spongebob.
Ne: Basically every stunut he has pulled to obtain the formula.
Si: Always looks back to what he he tried or learned before (and problably the reason he can't let go of the fact that Mr. Krabs is more successful than him), also ties in to his wallowing.
Fe: Needs validation 24/7 especially if he's failing 24/7, wallows like sin.
Karen: ENTP
Ne: She's much quicker in sorting out possible ways to obtains the formula, and unlike PLankton, can pin point the most efficient options (yet plankton never goes for them because he's never tried anything similar before).
Ti: As a computer, she's gotta compute; she's the one who checks Plankton's logical inconsistencies.
Fe: Although she doesn't necessarily ask for it, she expects to be acknowledged for her work and validated as a wife, which is where the marriage problems usually start.
Si: She probably has better things to do than watch Plankton fail again and again but in the end she stays with Plankton and sets out on what she was programmed to do: compute.
Gary: INFJ
Ni: He seems to base decisions off with his hunches. When Spongebob invaded his dream in that one episode, both his dream and way of explanation on what was happening to Spongebob resembled heavy symbolism. He can very easliy read people.
Fe: Gary is very openly affectionate to his owner along with other people, and is able to read their feelings very well.
Ti: Chances are the comebacks we never heard from Gary was his Ti, rebuking Spongebob's reasoning with rationality.
Se: Gary is very quiet and very aware of his environment, doesn't seem to appreciate loud noises or Spongebob's antics in the slightest.
Those are all the characters I can really type at the moment. Let me know what you think!