FWIW, from a 1981 FAA Legal Counsel opinion. The question dealt with 135 operations, but the answer references part 91 as well. The numbering of the regs has changed:
1. The aircraft is airworthy except the clock installed in the cockpit is inoperable. Would flight be allowed under Section 135.179 if there were no MEL and if the pilot in command possesses a reliable operating watch on his person? If so, who has authority to release the flight?
If the aircraft is type certificated for instrument flight rules, a clock is required by Section 91.33(d). However, even if the aircraft is not type certificated for instrument operations, other requirements apply.
Section 21.181 provides in pertinent part that an airworthiness certificate is effective so long as the maintenance, preventative maintenance, and inspections are preformed in accordance with Parts 43 and 91. Section 91.27(a)(1) provides in pertinent part that no person may operate an aircraft unless it has within it a current airworthiness certificate. Section 91.165 provides in pertinent part that no person may operate a civil aircraft unless it is in an airworthy condition, and that between inspections, defects in the aircraft must be repaired as prescribed in Part 43. Thus, to maintain the validity of the airworthiness certificate without a change to the type certificate, the clock must be operating for all operations, and operations with the clock inoperative would violate Sections 91.165, 135.3, and 135.143(a). A wristwatch would not substitute for the clock. The MEL and the letter of authorization for its use under Section 135.179(b) constitute a supplemental type certificate and provide a way to operate with the clock inoperative if the MEL so authorizes.