I am uncertain if you can splice *.t02 files directly but in the past I have created RINEX files from either TBC (by exporting ea. *.t02 to RINEX) or by using Trimble's ConvertToRINEX Utility* to convert the *.t02 files into RINEX files. Once in RINEX format, you can use TEQC Toolkit from UNAVCO to concatenate two or more RINEX files into a single RINEX observation. UNAVCO has created a TEQC Tutorial with instructions on how to use it.
I just tried to export two sequential t02 files from TBC v5 to see if it would just create one RINEX observation however it created 1 set of RINEX files for each t02 exported.
Be aware that TEQC is command-line oriented however I believe there is 3rd party GUI shell for it. I recall I may have seen the GUI on the NGS website (?). I mainly use TEQC with scripts I have written (great for drag & drop) so I have never tried GUI for it.
* Be sure to update your computer with the Trimble Configuration Utility before using ConvertToRINEX. See note on Trimble's ConvertToRINEX download page.
Regards,
John