You can refer to Nagarjuna's famous Seventy Stanzas
for an interesting argument on why our stream of thoughts in this lifetime must be a continuation from a previous life.
Regarding thought and brain development, "thought" and "consciousness" are rather loose terms.
It is only as we grow that we begin to "think" about something, and as we learn, we add to the pool of reference information that we use when we "think".
So, for example, a baby finds milk or some reasonable milk-like product satisfactory
even though there may not be any thought-associations. The baby doesn't know the word "milk" or even that the taste is good or bad. It just likes or dislikes the flavor and may respond positively to the parent's warm body temperature while feeding.
So, brain activity goes on in what you might call, by comparison, "pre-thought" activity, from which what we regard as "thinking" develops.
Likewise, although cognitive awareness may not jump from one body to another, there is no reason to think that the causes
of cognitive awareness are restricted to a physical body. If they were, perhaps there would be no memory, because the physical body you were born with died years ago, replaced slowly by one who is neither you nor an imposter.
Just as the radio signals do not stop merely because the radio has been destroyed, the ultimate state of things as they are, and as they appear, are all here ready to be reflected by the mind with the help of a brain mechanism. Reality is just floating all around us.
If your receptor is limited due to illusory clinging, you are a being wandering in a samsaric experience of your own creation. The essence of thoughts is dharmakaya, but due to a mind habitually clouded in confusion, it is seldom recognized, and instead, beings experience suffering.
A Buddha, on the other hand, is one who is perfectly liberated from confusion, and so is a perfect manifestation of dharmakya. A buddha's radio picks up not only perfect AM and FM reception, and all the short wave bands, but everything else on the electromagnetic spectrum including colors and x-rays.
Beam me up, Sakyamuni!