Is there a required appraisal engagement letter? We use a form that we prepared internally, which is very generic, but it gives the appraisers all of the information they need.

There is no engagement letter templete you are required to use. Each financial institution creates their own. From the guidance:

Interagency Appraisal and Evaluation Guidelines - 12-2-10

B. Engagement Letters

An institution should use written engagement letters when ordering appraisals, particularly for large, complex, or out-of-area commercial real estate properties. An engagement letter facilitates communication with the appraiser and documents the expectations of each party to the appraisal assignment. In addition to the other information, the engagement letter will identify the intended use and user(s), as defined in USPAP. An engagement letter also may specify whether there are any legal or contractual restrictions on the sharing of the appraisal with other parties. An institution should include the engagement letter in its credit file. To avoid the appearance of any conflict of interest, appraisal or evaluation development work should not commence until the institution has selected and engaged a person for the assignment.