I had a try with GDAL 2.4.0, released 2018/12/14 from OSGeo4W and then after update to GDAL 2.4.1, released 2019/03/15. I had no problem at all. I will make a new with your test once I have updated my GDAL to the same version that you havedata.
Result:
gdalbuildvrt test.vrt *.tif
0...10...20...30...40...50...60...70...80...90...100 - done.
gdalinfo test.vrt|more
Driver: VRT/Virtual Raster
Files: test.vrt
L333.tif
L334.tif
Size is 12000, 12000
Coordinate System is:
PROJCS["ETRS89 / TM35FIN(E,N)",
GEOGCS["ETRS89",
DATUM["European_Terrestrial_Reference_System_1989",
SPHEROID["GRS 1980",6378137,298.257222101,
AUTHORITY["EPSG","7019"]],
TOWGS84[0,0,0,0,0,0,0],
AUTHORITY["EPSG","6258"]],
PRIMEM["Greenwich",0,
AUTHORITY["EPSG","8901"]],
UNIT["degree",0.0174532925199433,
AUTHORITY["EPSG","9122"]],
AUTHORITY["EPSG","4258"]],
PROJECTION["Transverse_Mercator"],
PARAMETER["latitude_of_origin",0],
PARAMETER["central_meridian",27],
PARAMETER["scale_factor",0.9996],
PARAMETER["false_easting",500000],
PARAMETER["false_northing",0],
UNIT["metre",1,
AUTHORITY["EPSG","9001"]],
AXIS["Easting",EAST],
AXIS["Northing",NORTH],
AUTHORITY["EPSG","3067"]]
Origin = (260000.000000000029104,6714000.000000000931323)
Pixel Size = (4.000000000000002,-4.000000000000001)
Corner Coordinates:
Upper Left ( 260000.000, 6714000.000) ( 22d37'48.79"E, 60d29'25.49"N)
Lower Left ( 260000.000, 6666000.000) ( 22d41'14.15"E, 60d 3'38.39"N)
Upper Right ( 308000.000, 6714000.000) ( 23d30' 7.31"E, 60d30'58.14"N)
Lower Right ( 308000.000, 6666000.000) ( 23d32'51.92"E, 60d 5' 9.44"N)
Center ( 284000.000, 6690000.000) ( 23d 5'30.54"E, 60d17'20.43"N)
Band 1 Block=128x128 Type=Byte, ColorInterp=Palette
Color Table (RGB with 256 entries)
0: 0,0,0,255
1: 52,52,48,255
2: 64,48,24,255
...