How common is it for twins conjoined at the head to share thoughts and visual stimuli?
Short answer
Likely, the subject pool of craniopagus twins is too small to allow for scientific research. 

Background
As far as I can see after a cursory search, there is no scientific data available on the shared thoughts and experiences of craniopagus twins. Note that the incidence is only 1 in 10–20 per million births in the US. The rare occurrence, together wit the fact that neurosurgical advances increase the odds of successful separation (Browd et al., 2008) make them a truly rare phenomenon. On top of that, parents with conjoined twins will practically be living in the hospital with frequent, stressful visits to a variety of caregivers. In those difficult living situations likely the last thing they are waiting for is another white coat asking questions. In other words, the subject pool for research is minimized further by low response-rates when invitations for research participation are distributed (educated guess, being a parent).  

Reference
- Browd et al., J Neurosurgery: Pediatrics (2008); 1(1): 1-20