thank you for the pictures of the two flying pipits. Just commenting on the pictures (yes, a calling RTP can be identified with certainty, even in a vagrant context, so you have it allready!):
First picture shows good streaks to the breast, flank streaking could be bolder, but its within variation for RTP.
But: upperparts seems to plain and you should see streaks to the rump/uppertail-coverts.
Conclusion: plain upperparts and rump can easily explained by picture quality, where details are lost. But please compare here:
https://club300.de/gallery/photo.php?id=47501 and
https://club300.de/gallery/photo.php?id=47502 and
https://club300.de/gallery/photo.php?id=47894
Second bird lacks detail (no offense), but in an enlargement I can imagine sseing a flesh-orange base to the bill, better for Meadow Pipit (RTP has yellow base to the bill). I know, this is for sure to much digged out of this picture.
Conclusion? Both birds doesnt show
IDable Red-Throated-Pipits to me, because image quality prevents a safe identification and I can make out a feature (upperpart-streaking in the first, and bill colour in the second ) that cant be judged with certainty in this pictures, but would prevent me to name this birds as probable RTP in a vagrant (?) context. No offense as allways, as said you have it by hearing the call!