Keen to know about the method to perform sandhyavandanam during the asaucam period related to both birth and death.During a long-distance travel, can sandhyavandanam be performed mentally without taking a bath and without water?It is said that during asaucam period, it must be performed briefly with only 10 counts of Gayatri japam. Are the rules and regulations the same for asaucam related to both birth and death? Or do they vary? Are there any references to this in the scriptures? Want to know about this to observe them properly.

You have already pointed out in the 3rd query – it must be performed in an abridged format with 10 counts of Gayatri Japam during both birth and death-related asucam periods. It is not a practice to perform anganyAsa and karanyAsa. The mantra-s for japam and pranayamam must not be uttered through mouth and it is a rule to do them mentally.
During long-distance travels, sandhyavandanam can be done mentally with the relevant mantras. Even so, after reaching a place where water is available, the previous day sandhyavandanam is also performed.
The rules and regulations are the same for asaucam periods related to birth and death. It is not clear what you mean by notes/references.