Try something like below. I don't know where User.AccessID comes from so I just called it AccessID and set it to 10 for testing.
Any time the recordsource is altered, a form requery is required.
Code:
Option Compare Database
Option Explicit
Private Sub runSearch_Click()
Dim strText As String
Dim strSearch As String
Dim accessID As Integer
strText = Trim(Me.txtSearch)
accessID = 10
Select Case accessID
Case Is = 1, 7, 10, 11
strSearch = "Select * from Personnel where ([personnel-Unit] = ""Michigan"") and " _
& "(([personnel_Surname] like ""*" & strText & "*"") " _
& "or ([personnel_Inits] like ""*" & strText & "*"") or " _
& "([personnel_Title] like ""*" & strText & "*"") or " _
& "([personnel_L6] like ""*" & strText & "*""))"
Case Is = 3, 4, 5
strSearch = "Something else"
Case Else
End Select
Debug.Print strSearch
Me.RecordSource = strSearch
Me.Requery
End Sub