Short answer: Usually for any amount over the guaranteed issue limit, for elections made after the first eligibility window, and for later increases. The rules are in the policy: Texas law requires a group life policy to state the conditions under which the insurer may require evidence of insurability.
Group life is sold with a guaranteed issue amount: coverage up to that amount is issued without health questions to eligible employees who enroll when first eligible. Amounts above it, late elections, and increases generally require evidence of insurability (a health questionnaire, sometimes more), and the carrier can decline the excess. Exact limits and late-entrant rules vary by carrier and contract.
Two practical points. First, an employee who waives at hire and enrolls at a later open enrollment is often treated as a late entrant who must qualify medically for everything. Second, an amount pending evidence of insurability is not in force until the carrier approves it, so payroll should not deduct for it until then.
The Texas Insurance Code requires every group life policy to state the conditions, if any, under which the insurer can require evidence of individual insurability, so the certificate is the place to check.