In Romans 2:15 and 9:1 Paul speaks of the conscience bearing witness/testifying on behalf of someone. These phrases are:
(2:15) συμμαρτυρούσης αὐτῶν τῆς συνειδήσεως
“their conscience bearing witness”
(9:1) συμμαρτυρούσης μοι τῆς συνειδήσεώς
“my conscience bearing witness”
The first reference is found in the context of pagans who do not have the Law doing those things required by Law instinctively. The second reference is Paul preparing to inform his readers that he would be anathema from Christ if it would result in the reconciliation of his kinsmen to Christ (ηὐχόμην γὰρ ἀνάθεμα εἶναι αὐτὸς ἐγὼ⸃ ἀπὸ τοῦ Χριστοῦ).
In 2:13-15 some have read this as Paul alluding to some sort of “natural law,” and this may be true, but there is an echo of Jeremiah 31:31-33 that shouldn’t be overlooked. In Jeremiah 31 the prophet speaks of a time when the New Covenant will be written on the hearts of the people. It seems to me that Paul is proposing that some non-Jews might be entering the New Covenant, where the Law is written on their hearts, and therefore the old badges of the Covenant, like circumcision, do not function to include or exclude people.
We know that Paul connects the Spirit will the New Covenant in this epistle and others. Passages like Joel 2:28-32 provided helpful language for describing how the Spirit would make new people, the sort of people who do not need a Law written on stone, but one written on a heart (e.g., Ezekiel 36:26). I think it is fair to assume that Paul has the Spirit in view in 2:13-15, even if the Spirit is not mentioned specifically.
The Spirit is mentioned in 9:1. The Spirit testifies with Paul that what he is about to say is not a lie. This leads me to connect these passages: Paul presents one’s conscience as bearing witness. In 2:15 the final verdict is not given: the thoughts of a person accusing or defending them in anticipation of the day when God will judge through Jesus (v. 16). If the Spirit is “present” in this scenario, though the verdict isn’t given by Paul, one might suggest that it can be known. These pagans will receive a favorable verdict. Similarly, Paul is confident that his conscious will be vindicated as he testifies in the Holy Spirit.
I haven’t explored further conceptual connections, but I do find this one interesting.