Red hair origin is always interesting. It appears it was present in europe before the R1b invasions.
According to this site which lists pigmentation of many ancient samples (don'tknow how reliable it is)https://genetiker.wordpress.com/pigmentation/
the oldest one is found in Mesolithic romania
[TABLE="width: 390"]
[TR]
[TD="width: 38"] I4582
[/TD]
[TD="width: 100"] Romania MHG
[/TD]
[TD="width: 99"] 7021–6473 BC
[/TD]
[TD="width: 55, bgcolor: #d7a57a"] Medium
[/TD]
[TD="width: 27, bgcolor: #c80815"] Red
[/TD]
[TD="width: 33, bgcolor: #318ce7"] Blue
[/TD]
[/TR]
[/TABLE]
followed by a corded ware sample
[TABLE="width: 422"]
[TR]
[TD="width: 68"] Spiginas 2
[/TD]
[TD="width: 133"] Corded Ware LT LN
[/TD]
[TD="width: 99"] 2130–1750 BC
[/TD]
[TD="width: 25, bgcolor: #f4f4f4"] NA
[/TD]
[TD="width: 27, bgcolor: #c80815"] Red
[/TD]
[TD="width: 33, bgcolor: #318ce7"] Blue
[/TD]
[/TR]
[/TABLE]
with a huge gap of 5000 years
and then a bell beaker sample
[TABLE="width: 415"]
[TR]
[TD="width: 38"] I2787
[/TD]
[TD="width: 131"] Bell Beaker HU CA
[/TD]
[TD="width: 99"] 2457–2201 BC
[/TD]
[TD="width: 35, bgcolor: #fff4f2"] Light
[/TD]
[TD="width: 27, bgcolor: #c80815"] Red
[/TD]
[TD="width: 47, bgcolor: #964b00"] Brown
[/TD]
[/TR]
[/TABLE]
and a Jordan(!) one.
[TABLE="width: 351"]
[TR]
[TD="width: 38"] I1730
[/TD]
[TD="width: 80"] Jordan EBA
[/TD]
[TD="width: 99"] 2489–2299 BC
[/TD]
[TD="width: 35, bgcolor: #fff4f2"] Light
[/TD]
[TD="width: 27, bgcolor: #c80815"] Red
[/TD]
[TD="width: 33, bgcolor: #318ce7"] Blue
[/TD]
[/TR]
[/TABLE]
Thereare a couple more of bell beaker samples. I would tend to think that the Czechia stroke ornament sample got it from a source similar to the romania mesolitic hunter gatherer and then the Steppe invaders got it from that and spread it. What do you think? The area of Stroke-ornamented ware culture is not far from romania and is about in the corded ware area.
All the old samples concentrate in central-east europe (aside from the jordan one).