There isn't much we can do to see if viruses persist in the brain besides an immediate autopsy(which has its flaws). One promising thing I've seen is scanning someone's brain to see brain cell amyloid plaque formations which may indicate an immune response / protection from these viruses. This also could be a means to better understand other diseases like Alzheimer's.
But for other brain researchers with regards to covid/long covid, there isn't strong evidence yet to suggest it can reach the brain outside of the current autopsy studies: