I'm not sure that parking with Global is
exactly what you want. It may be.
If you go to the Global site and check "About Us" you will find that they do not have a parking lot. They arrange for you to park on a hotel parking lot and give you a ride to the cruise terminal. Now they are cheap, advertising prices as low as $3.99 a day, although I expect you will find your price higher.
The official Tampa Port Authority parking garage is operated by Channelside Parking and the rate is $15 a day. The enclosed garage, attended 24 hours a day and equipped with CCTV cameras is directly across the baggage drop off point for terminals 2 & 3. You can drop your bags, drive across the street and park and then walk back to check in.
The Channelside Parking site is at
Parking Info - Tampa Port Authority - Channelside Parking Garage - Cruise Parking - Garrison St Lot
Enlarge the map on this page to see terminal details. The baggage drop off point is near the circle marked as cruise terminal 2.
There are three places that advertise off site parking for $7.99 a day. Two of them, Airandcruise Parking and Premier Parking have the same address so I am only giving one web address
Port of Tampa discount seaport parking - Premier Parking USA
The third, Capital Parking advertises at
Cruise Parking for the Port of Tampa, Florida | Services
No matter which you choose you might want to drop your bags at the terminal baggage drop off point before parking so you don't have to bother with baggage from the parking lot to the terminal.
I have only used the official parking garage, never any of the off site ones.
Enjoy your cruise.