To use both your Connect personal and a Connect functional account in the Google Web App (GWA), you can save yourself an extra login by "delegating" access to your functional account to your personal account. To do this, log into your functional account in GWA and click Settings -> Accounts. In ‘Grant access to your account’, click 'Add another account', enter your @ucsb.edu email address, and follow the steps.
Then, log into your personal account in GWA and click on your email address in the upper right corner. Click 'Add account' and enter your functional account's @ucsb.edu address and password. Now whenever you click on your personal account name in the upper right corner, you will see the functional account also listed there. To open it, just click on it
If you are using Outlook as your primary client, see the instructions for delegating access in Outlook.