I have sql2k16, SP2, CU10. Default instance and 1 named instance. SQLAgent runs fine with the default instance but never can start in the named instance.
I red/followed almost all threads about this subject, no way, as soon it is started, 50 seonds later it stops. Here is the output from SQLAGENT.OUT (I tried different logins domain and locals all with sysadmin privilges, tried also NT SERVICE\SQLAgent$SC2K12, activated named pipes, remote access is allowed, disabled/renabled/ DisableAgentXPs.........)
2019-11-05 18:24:29 - ? [100] Microsoft SQLServerAgent version 13.0.5492.2 (X64 unicode retail build) : Process ID 2676
2019-11-05 18:24:29 - ? [495] The SQL Server Agent startup service account is NT SERVICE\SQLAgent$SC2K12.
2019-11-05 18:24:59 - ! [150] SQL Server does not accept the connection (error: 67). Waiting for Sql Server to allow connections. Operation attempted was: Verify Connection On Start.
2019-11-05 18:24:59 - ! [000] Unable to connect to server 'SQL2K12/SC2K12'; SQLServerAgent cannot start
2019-11-05 18:25:05 - ! [298] SQLServer Error: 67, Named Pipes Provider: Could not open a connection to SQL Server [67]. [SQLSTATE 08001]
2019-11-05 18:25:05 - ! [165] ODBC Error: 0, Login timeout expired [SQLSTATE HYT00]
2019-11-05 18:25:05 - ! [298] SQLServer Error: 67, A network-related or instance-specific error has occurred while establishing a connection to SQL Server. Server is not found or not accessible. Check if instance name is correct and if SQL Server is configured
to allow remote connections. For more information see SQL Server Books Online. [SQLSTATE 08001]
2019-11-05 18:25:05 - ! [382] Logon to server 'SQL2K12/SC2K12' failed (DisableAgentXPs)
2019-11-05 18:25:05 - ? [098] SQLServerAgent terminated (normally)