Hi Daniel,
The account that tries to open the connection to the network share "\\server\backup" is the account that runs the MaxDB services. You can check it in the Windows Services (Start > run > Services.msc) nad find out the MaxDB service. It's usually the Local System.
You can also check with the command #sc qc "SAP DBTech-<SID>" where your <SID> is the db name. The "SERVICE_START_NAME" is the account.
If it's Local System, then the account that tries to connect to the network share is the Computer account:
Security ID: DOMAIN\COMPUTERNAME$
Account Name: COMPUTERNAME$
Account Domain: DOMAIN
Logon ID: 0x000000
It would be the case to change the user that starts the MaxDB Service to a Domain user that you can provide access in the network share or add the computer account DOMAIN\COMPUTERNAME$, but I don't think the second is the best approach.
Check the SAP Note 2068537 - Backup on network drive (Microsoft Windows) on detail and also 1377148 - FAQ: SAP MaxDB backup / recovery, point 24.
Regarding the question about the "exact time", I don't understand the purpose.
Regards,
Luis Darui