B737 Undifferentiated or Other Model
Air Traffic Control Developmental
Situational Awareness
ATC Issue All Types; Conflict Ground Conflict; Less Severe; Deviation / Discrepancy - Procedural Clearance
General None Reported / Taken
ATC Equipment / Nav Facility / Buildings; Human Factors; Environment - Non Weather Related
I taxied the SF34 to Runway 19L via Taxiway C. A few minutes later the B737 called ready to taxi. I issued taxi instructions to the B737 to Runway 19R via C; B8; B and V Taxiway. When I issued this; I had the B737 insight; I did not see any other aircraft in his way. The SF34 that I taxied; I did not see; I assumed he had already departed. The SF34 was actually on Taxiway C; but he was obstructed from my view by the TDW display monitor. I didn't move from the spot that I was standing at because to my right was the console and to my left was my chair that I offered to other personnel. The B737 assumed that I had instructed the SF34 to give way to him; and began to taxi out as instructed. The SF34 continued to taxi. The B737 had to stop and give way to the SF34. I could have moved around and better scanned the taxi route prior to issuing the taxi clearance. I also recommend that the TDW display be lowered; so that the view of a major taxiway and the main entering/exiting point for taxing aircraft is not obstructed.
Pushed out of gate. I received clearance from Ground Control to taxi via Taxiway C; B8; B; M; V to Runway 19R. There was no mention of any traffic to follow or be aware of. Just prior to taxing onto Taxiway C from the ramp heading northeast; I noticed a twin engine turboprop aircraft on my right taxiing north on C. It did not appear that we would be able to get in front of him nor was the turboprop aircraft slowing down; so I told the Captain to stop; which he immediately did. The Captain talked to Ground Control to ensure once again what our taxi clearance was and to inform Ground about the turboprop. Our taxi clearance was as previously received. The Captain checked with the flight attendants to ensure they were okay. He informed me that they were okay.
TPA Controller experienced a developing ground conflict when failing to observe a taxiing aircraft.  The reporter listed tower equipment placement and not moving around as contributing factors.