TIFF files sems to be wrong, they do not have EXIF, but ICC instead

[Fojtik]

The tiff images are demonstrating ICC profiles, not EXIF. I need TIFF with EXIF inside.

#define TIFFTAG_EXIFIFD 34665 /* Pointer to EXIF private directory */
/* tag 34750 is a private tag registered to Adobe? */
#define TIFFTAG_ICCPROFILE 34675 /* ICC profile data */

Tag=256, field=3, value=635,long2=1
Tag=257, field=3, value=348,long2=1
Tag=258, field=3, value=4,long2=4
Tag=259, field=3, value=5,long2=1
Tag=262, field=3, value=2,long2=1
Tag=273, field=4, value=284534,long2=7
Tag=274, field=3, value=1,long2=1
Tag=277, field=3, value=4,long2=1
Tag=278, field=3, value=51,long2=1
Tag=279, field=4, value=284562,long2=7
Tag=284, field=3, value=1,long2=1
Tag=317, field=3, value=2,long2=1
Tag=338, field=3, value=1,long2=1
Tag=339, field=3, value=4,long2=4
Tag=34675, field=7, value=284598,long2=3940

[Fojtik]

The file "kosticky2.tiff" in attachment is the only TIFF file that perhaps embedd part of EXIF. The exif is not fully loaded, EXIF must be fully dissasembled and assembled anew. Even this costed me several hours of work.
Kosticky2.zip

The attached image "kosticky2.tiff" really contains tag 34665:
<<< CONVERT >>> Convert picture format (c)1997-2023 F&TSoft, version 2.65
Loading
5D602 Tag=256, field=3, value=2312,long2=1
5D60E Tag=257, field=3, value=1734,long2=1
5D61A Tag=258, field=3, value=55006,long2=3
5D626 Tag=259, field=3, value=7,long2=1
5D632 Tag=262, field=3, value=6,long2=1
5D63E Tag=269, field=2, value=383424,long2=14
5D64A Tag=273, field=4, value=382744,long2=13
5D656 Tag=274, field=3, value=1,long2=1
5D662 Tag=277, field=3, value=3,long2=1
5D66E Tag=278, field=3, value=144,long2=1
5D67A Tag=279, field=4, value=382692,long2=13
5D686 Tag=284, field=3, value=1,long2=1
5D692 Tag=297, field=3, value=0,long2=2
5D69E Tag=305, field=2, value=383438,long2=71
5D6AA Tag=339, field=3, value=55116,long2=3
5D6B6 Tag=347, field=7, value=382850,long2=574
5D6C2 Tag=532, field=5, value=382802,long2=6
5D6CE Tag=34665, field=13, value=382308,long2=1