Richard's Pipit is a regular winter visitor in my area and I think I have good experience with this species. TBH, the bird in the two photos here did not strike me as Richard's. Reasons being -
1) Face looks wrong for Richard's. A Richard's should have a broad buff supercilium behind eye.
Please refer to
Richard's Pipit Macaulay Library ML409835231 for a Richard's at similar angle to OP's 2nd photo.
2) Bill looks weak. Even though it is open in both photos, a Richard's should have a thicker lower mandible and overall, its bill should have more pink/yellow.
Please refer to
Richard's Pipit Macaulay Library ML290846731 for a side profile of bill, in closed position though.
3) Its posture and structure look doubtful. Even from this angle, a Richard's should look more upright. The birds that winter in India, they are extremely shy on their wintering grounds and barely allow close approach. Even from a distance, if it spots a human, it goes into an alert upright position and quickly flies away.
Another photo. Somewhat similar to OP's 1st image.
Richard's Pipit Macaulay Library ML426846681
Based on what I see in these images, I would incline towards a Meadow Pipit in the absence of call record.