After doing a quick Google search for
Plesk "Application Vault" +osTicket +email +configuration
I may have found your problem, it is the Plesk Application Vault that probably removes this section from your install.
You see installers like the Plesk Application Vault, Fantastico and Softalicious select Open Source applications that they can modify and distribute. Plesk even have a distribution of osTicket that sounds very impressive integrating with Plesk as the support system of choice so server admins can support customers and resellers customers with the single osTicket installation.
I am under the belief that when installed from the Application Vault you need to run osTicket with email piping set up to postfix Plesk distribution, if this is the case you most likely will not be able to use this osTicket version with Gmail.
If you want to use osTicket with email piping (maybe use a sub-domain that uses the internal server for email - e.g. @[deleted]), check out (this information/tutorial). Be warned, read this in its entirety, you need the right permissions and some knowledge to use this solution so it may not work.
I hope this is helpful and sorry for what seems to be bad news for you.