For now I will assume that you are running Premiere Elements 12 on Windows 7, 8, 8.1 64 bit computer. Have you updated 12 to the 12.1 Update using an opened project's Help Menu/Update. If not, please do so.
Now for your immediate issue which I think should be resolved quickly.
You are apparently in the Quick workspace of the program, under the Transitions Tab. You need to be working in the Expert workspace. When you do you will find all your video and audio transitions.
For several types of items, the Quick workspace does not have all the items available that are found in the Expert workspace.
Please check it out and then let us know the results.
Thank you so much for the quick reply! You are of course 100% spot on. What can I say, that's what happens when you use a piece of software only occasionally as opposed to regularly....I have demonstrated myself a as a complete noob! Thanks again, much appreciated.
Please never hesitate to ask questions and to ask for clarification. The program opens by default to Quick workspace and, if you have had limited
use of the program, your question was very appropriate. Occasionally some of the program's feature will good missing. The Music Score and Sound Effects under the Audio tab occasionally appear long after the program is installed. And, if you do not have the latest version of QuickTime installed on your computer along with Premiere Elements, the QuickTime presets go missing. And, generally speaking, there are many Expert workspace only items.
Bottom line, you did well asking your question, and we were glad for the opportunity to be of assistance.
Best wishes with your Premiere Elements projects