Section 23A. No trustee of any public institution of higher education operated by the commonwealth shall be eligible to be appointed to or hold any other office or position with said institution for a period of three years next after the termination of his services as such trustee, or in the case of an elected student trustee at said institution, for a period of one year next after the termination of his services as such trustee; provided, however, that any such elected student trustee may accept and hold part-time employment at said institution while a student thereat, and provided further, that a trustee may be appointed to or hold an unpaid office or position with said institution after his services as such trustee.