Eligibility is defined by the official program terms, not by the other spouse's TN offer. Read those terms for who may apply and who may accompany; a job offer neither qualifies nor disqualifies the spouse.
The TN offer is irrelevant to the Gold Card question
TN eligibility turns on Canadian or Mexican citizenship, a listed profession and a prearranged professional job; it has no bearing on whether the other spouse can apply under the Gold Card framework. The Gold Card's own terms, published on the official page, decide who may be a principal applicant and who may accompany that person as family. The couple should read those terms for the spouse's own situation: her citizenship, whether she would apply as the principal, and whether the program's family provisions would cover the nurse instead.
If the answer is that only one principal is contemplated and the other joins as family, the household must then check what the family member is permitted to do, since the official material rather than assumption governs work rights. Treat any silence in the official terms as an open question to be resolved before proceeding, not as permission.