I bought one of my ex-rides, Nissan Tiida, in a similar manner from a family.
Car was there, but smart card was not received because of closure of Excise office due to COVID-19, and lock downs.
Procedure adopted was: I made full payment and took custody of the car. The owner, which was a lady, provided me with 02 receipts in original, one regarding payment of token taxes, etc. till June 2020, and 2nd one regarding receipt, which you get when you had finally applied for transfer of ownership. When she received the smart card, she informed me and I collected it from her, and at the same time, I also got her valid Biometric slip.
I did not withheld any amount, in this particular case, due to valid reasons, however, if there could have been no educated family, I would have definitely withheld some amount, or not buy car altogether.
I hope, all above helps. Thank you.