linq Group By and take first and lats records

Well, having (let use named tuple to demo):

var resultList = new (string Plate, string Brand, string Model, DateTime InsertDate)[] {
  ("99AA111",  "Tesla",  "S",       new DateTime(2022,01,17, 04,00,00)),
  ("99AA111",  "Tesla",  "S",       new DateTime(2022,01,17, 04,30,00)),
  ("99AA111",  "Tesla",  "S",       new DateTime(2022,01,17, 05,00,00)),
  ("59TA3312", "Nissan", "Skyline", new DateTime(2022,01,17, 04,00,00)),
  ("59TA3312", "Nissan", "Skyline", new DateTime(2022,01,17, 04,30,00)),
  ("129EA512", "Subaru", "Impreza", new DateTime(2022,01,17, 03,30,00)),
};

You can GroupBy twice:

var groupedResult = resultList
  .GroupBy(item => item.Plate)
  .SelectMany(group => group
     .OrderBy(item => item.InsertDate)
     .Select((item, index) => (item: item, index: index / 2))
     .GroupBy(pair => pair.index)
     .Select(g => (
        Plate: g.First().item.Plate,
        Brand: g.First().item.Brand,
        Model: g.First().item.Model,
        FirstPhotoDate: g.First().item.InsertDate,
        SecondPhotoDate: (g.Count() == 1 ? null : (DateTime?)(g.Last().item.InsertDate))
     ))
   );

Let's have a look:

string report = string.Join(Environment.NewLine, groupedResult
  .Select(r => $"{r.Plate,-8} : {r.Brand,-6} : {r.Model,-7} : {r.FirstPhotoDate} : {r.SecondPhotoDate}"));

Console.Write(report);

Outcome:

99AA111  : Tesla  : S       : 17.01.2022 4:00:00 : 17.01.2022 4:30:00
99AA111  : Tesla  : S       : 17.01.2022 5:00:00 : 
59TA3312 : Nissan : Skyline : 17.01.2022 4:00:00 : 17.01.2022 4:30:00
129EA512 : Subaru : Impreza : 17.01.2022 3:30:00 :