I’ve been saving this update about the American teacher because I wanted to hear more, but given the recent resurgence of interest 
in Jump Start, I’ll share it now.
He lost the final appeal, and the Supreme Court’s reasoning is basically a condensed version of what the High Court said (nothing unusual).
I was looking forward to this because it might have shed some light on the 1946 Treaty of Friendship, Commerce and Navigation Between the Republic of China and the United States of America, Art. 2 Par. 2 & 3 of which are rather interesting:
There’s an inconsistency between Art. 52 of the Employment Service Act and Art. 9 of the Labor Standards Act, so even though an employment* contract can be for an indefinite (permanent) term, a foreigner’s employment contract cannot, unless the foreigner is subject to ESA Art. 51 Par. 1 (including permanent residents). Mr. American Teacher’s contract had no visible expiration date, and he was married to a Taiwanese, but nonetheless he was not a permanent resident and not subject to Art. 51 at the time of the disputed resignation, so the contract was deemed a fixed term contract in accordance with Art. 52. Presumably, he argued that this is inconsistent with the Treaty, yet the Supreme Court merely stated that Art. 6 (not Art. 2) of the Treaty is inapplicable because it concerns due process, protection of life and property, and so on, not employment rights.
*(the distinction between “labor” and “employment” is irrelevant in this case)
The SC also said Interpretation #726 of the Council of Grand Justices is inapplicable because it concerns Art. 84-1 of the LSA, to which buxiban teachers are not subject. Presumably, his point in bringing up Int. 726 was that he was claiming the work permit issue of the ESA is purely administrative and that therefore a contract can still be civilly valid even if it’s administratively invalid, but the SC did not directly address this. (The full text of Int. 726 including concurrence & dissent is quite long, and I haven’t read the whole thing yet.)
The SC also found the Consumer Protection Act and the Fair Trading Act inapplicable because the two sides didn’t have a consumer relationship. Iirc the point of bringing these up in the first appeal was that consumers can withdraw consent in a timely manner, the claim being that this should apply to employment contracts and disputed resignations mutatis mutandis.
He also argued that the contract’s loss of validity upon completion of the term (the term being set by law but not disclosed in the contract itself) constituted obvious unfairness and was therefore invalid due to Art. 247-1 of the Civil Code. The SC found that loss of validity upon completion of the term was the “natural result” of the contract, so Art. 247-1 is inapplicable.
His case seems to have been doomed anyway, because he simply didn’t have enough evidence to prove he was coerced into signing the resignation letter. The SC (which of course merely reviewed the facts found by the first two courts) did not find the inconsistency between statements by different witnesses sufficient to prove the employee was coerced into resigning or fired by the employer (至[…]書寫之具結書，內容與上開證人之證述不符，不足據以認定上訴人係遭脅迫辭職或解僱).
So, the company (or rather the buxiban, technically) wins and can defend its oh-so-squeaky-clean reputation. 