Whether the spouse's own work plans fit the timing. A spouse in valid L-2S status is authorized to work incident to that status, and an employment authorization document is not universally required, but a prospective employer still needs acceptable documentation when completing hiring paperwork.
Prepare for the hiring paperwork question
Employers vary in how familiar they are with L2 employment authorization, and an unfamiliar recruiter can slow an otherwise straightforward hire. Have the spouse know which documents evidence their authorization and be ready to point to the official guidance rather than argue from memory. Children in L2 are not work authorized, which matters for teenagers expecting part-time work, and only unmarried children under 21 are eligible for L2 at all.
Add one further preparation for a two-career household: agree what the spouse will say and show before the conversation happens, and agree it in writing. A recruiter encountering an unfamiliar arrangement will often ask a question the candidate cannot answer on the spot, and the moment passes badly. Have the spouse hold a short written summary of what their status permits and which document evidences it, and know where the official guidance can be found rather than relying on recollection.
Then decide who in the household chases each step, since the spouse's position generally follows the principal's and a delay in one becomes a delay in both. Hypothetical example: a database migration specialist's spouse, a data scientist, keeps a one-page note and the relevant document reference in the same folder as their portfolio, and an offer that might have stalled for a fortnight is settled in a single email exchange.