If one believes that cognition is self-aware, one believes that within a cognitive act one does not seize only an object but also the cognition itself. Prābhākaras (see Rāmānujācārya's Tantrarahasya, chapter 1) maintain that one is at the same time aware of an object, of the subject perceiving it and of cognition itself. Buddhists of the Dignāga-Dharmakīrti tradition claim that there is no "subject" beyond cognition and hence maintain that cognition is just aware of itself. Does this mean that it is also aware of its contents?
That is, is svasaṃvedana (self-awareness) of the form "self-awareness of cognition of something" or is it just "self-awareness of cognition"? If the first, is this "something" specified as it would be in the final piece of cognition of an (apparently) external object or not? Does cognition perceive oneself as "cognition of a patch of blue"? or just as "cognition of something" (indeterminate)?
I would be happy with both options and I could even acknowledge the possibility of the third one mentioned above ("self-awareness of cognition"), although it is hard to figure out how the object form (grāhya) can be separated from the cognition.
Rāmakaṇṭha seems to maintain an extreme position: svasaṃvedana is just the nature of consciousness. Hence, it does not entail any object as its content. It is, moreover, present even in deep sleep, coma, and "within thoughts". The latter example refers to a typical Śaiva argument in favour of a permanent self (see Vasugupta's Śivasūtra and commentaries thereon): one needs an underlying self enabling one to shift from one thought to the other. This leads me to the following conclusion: Rāmakaṇṭha held this strange position (self-awareness of cognition qua cognition but without any cognised content) because he just substituted "consciousness" for any occurrence of "self" (ātman) (on this point, see Watson 2006 who nicely explains how Rāmakaṇṭha countered Buddhists by accepting all their arguments in favour of cognition alone and then explaining that cognition IS the self). Then, he assumed that self-awareness is co-essential to consciousness. Hence, his arguments in favour of self-awareness being always present are just to be thought of as arguments in favour of the continuous presence of a self which consists in cognition (of what? obviously of oneself, hence, it consists in self-awareness).