The actions took place during a special called meeting via telephone conference on April 3.
City Manager Clint Garza said the Texas state code requires council to accept Goodwin's written resignations, or eight days could pass with no action and it would be accepted.
There were three applicants for Goodwin's spot on the EDB, but council appointed All Star Burger owner Shane Street.
Council Member Andrea Willott said one direction council wants to take is to add more business owners to the EDB, to which Council Member Andrew Clark agreed.
"I think it's important we broaden what we're doing on the EDB to include ... those on the front lines of our economy, so to speak.
Though council endorsed Street, the bulk of public commenters endorsed another applicant, Carrell Killebrew, to take Goodwin's spot on the EDB.
Council also named Goodwin's replacement for his place on the WTCPUA, Jack Creveling, who is also a director on the EDB.
Though council accepted Creveling's appointment on the WTCPUA, he will also need unanimous approval from the Lake Pointe Municipal Utility District and Hays County.
Of note, Council Member Jon Cobb, who abruptly resigned from council during a March 28 special meeting, was present in his official capacity as a council member during the April 3 meeting.
Garza explained April 1 only a written resignation can be accepted by Bee Cave officials.
Bee Cave resident Ed Crack said during public comment that he did not understand why Cobb was present as a council member since he resigned March 28.
Congruent with Garza's earlier explanation, Mayor Kara King confirmed Cobb is still on council because he never submitted his resignation in writing.