Putting bits and pieces together I found the following answer by BruceCran:
Any timestamp server can be used: I recently switched from my issuer's
timestamp server to Verisign since I found that GlobalSign's server
was unreliable. Furthermore, Thawte don't run their own timestamp
server but recommend people to use Verisign's.
So, yes I assume I can use any timestamp server.
As for what a timestamp server does, it is explained by Comodo:
Since key pairs are based on mathematical relationships that can be
cracked with a great deal of time and effort, it is a well-established
security principle that a digital certificate should expire. Your
Digital ID will expire one year after it is issued. However, most
software is intended to have a lifetime of longer than one year. To
avoid having to resign software every time your certificate expires,
companies have introduced time stamping services. When you sign code,
a hash of your code will be sent to Certification Authority to be time
stamped. Once your software has been time stamped, you will not need
to worry about resigning code when your Digital ID expires. Microsoft
Authenticode allows you to time stamp your signed code so that
signatures will not expire when your certificate does.
So your certificate expires, but your code doesn't.