Is it possible for me to sit CASA ‘basics’ exams anywhere?

No. As of 1 July 2021, it has no longer been possible for CASA to issue an aircraft engineer’s licence through the submission of the CASA “basics” combined with SOE (Schedule of Experience). However, any “basics” you have completed can be used to grant credit towards certain topics within the CASA “modular” exams through an RPL process. (Reference: https://www.casa.gov.au/licences-and-certificates/maintenance-engineers/recognition-prior-learning-rpl-assessment-casa-basics)

See the FAQ What good are my Basics Results?