Gaits and anti-predator displays, compared between deer (Odocoileus) in North America and impalas (Aepyceros) in Africa

There is an adaptive trend among the ruminants of the world, as follows.

Species adapted to dense cover tend to have

inconspicuous colouration (particularly on the hindquarters),
a halting gait, viz. the semi-crosswalk,
a lack of stotting (strenuous displays of individual fitness, dissuasive to scanning predators), and
non-gregarious society.

A typical example is bushbucks (Tragelaphus, https://www.inaturalist.org/taxa/1431867-Tragelaphus-sylvaticus and https://www.inaturalist.org/taxa/42341-Tragelaphus-scriptus).

By contrast, species adapted to short, sparse vegetation tend to have

conspicuous colouration (particularly on the hindquarters),
a smooth gait, viz. the amble,
stotting, and
gregarious society.

A typical example is the springbok (https://www.inaturalist.org/taxa/42283-Antidorcas-marsupialis).

Intermediate species show intermediate traits.

In the context of this adaptive axis, certain anomalies emerge. The following are prime examples.

Deer of genus Odocoileus in North and central America, and impalas (Aepyceros) in southern and East Africa, are comparable. Both fall into the intermediate part of the axis described above.

Both are associated with some woody cover, as opposed to treeless grassland. Accordingly, both are somewhat gregarious.

Both have

medium body mass (about 50 kg),
unremarkable body-proportions, and
fairly nondescript colouration on forequarters and torso.

However, two incongruities emerge, as follows.

Firstly, Odocoileus deer combine

a halting walking gait, linked to cover-dependence and non-gregariousness, with
conspicuous colouration on the hindquarters, linked to open environments and gregariousness.

By contrast, impalas combine

a smooth walking gait, linked to open environments and gregariousness, with
inconspicuous colouration on the hindquarters, linked to cover-dependence and non-gregariousness.

Secondly, both genera have stotting displays. However, the gaits used are surprisingly different.

Odocoileus deer display by

stiff-legged serial bouncing in the case of Odocoileus hemionus (https://www.youtube.com/watch?v=49fz_WKBrXo), accentuated by pale pelage on the rump,
initial leaping in the case of Odocoileus virginianus, accentuated by pale pelage, activated on the tail and buttocks, and
demonstrative walking/foot-stamping, in both spp. (https://www.youtube.com/watch?v=rmmpBklsfUY and 'alarm walking', https://academic.oup.com/jmammal/article/89/3/636/861999?login=false).

By contrast, impalas display by

kick-stotting (apparently only in reaction to the African hunting dog, Lycaon pictus), in which the tail is displayed but not particularly conspicuously (https://www.youtube.com/shorts/Ul5PgndSuE8 and https://www.sciencephoto.com/media/953676/view/black-faced-impala-female-jumping and https://www.shutterstock.com/image-photo/impala-aepyceros-melampus-female-jumping-on-2322843111 and https://www.shutterstock.com/image-photo/three-jumping-impala-lambs-center-one-52838104 and https://www.shutterstock.com/image-photo/impala-athletics-585239423 and https://www.shutterstock.com/image-photo/dancing-impalas-on-move-537287350 and https://www.shutterstock.com/image-photo/impala-pronking-morning-light-on-serengeti-756579790 and https://www.shutterstock.com/image-photo/flying-impala-wild-1981885313 and https://www.shutterstock.com/image-illustration/young-impala-female-playing-jumping-green-681128110), and
bounding, in which the tail is negligibly displayed (https://www.gettyimages.ie/detail/photo/male-impala-antelope-in-mid-leap-royalty-free-image/540562926?phrase=impala+the+animal&adppopup=true and https://www.shutterstock.com/image-photo/jumping-impala-africa-1266703183 and https://www.gettyimages.com.au/detail/video/slow-motion-tracking-shot-profile-herd-of-impalas-stock-video-footage/89-59 and https://www.shutterstock.com/image-photo/impala-jumping-avoid-being-caught-greater-40298869 and https://www.shutterstock.com/image-photo/common-impala-kruger-national-park-south-1164360943).

Stating the puzzle concisely:
The deer referred to are incongruently demonstrative, whereas impalas are incongruently non-demonstrative.

Before attempting to explain this puzzle, let us examine the evidence by means of photos/video clips.

The following show the semi crosswalk, which is

associated with cover-dependent ruminants, and
in the case of Odocoileus has been 'exaggerated' into demonstrative walking.

What is remarkable is that a halting gait, allowing the animal to 'freeze' with two legs in the air in order to blend into the background when hearing or seeing something suspicious, has been converted from an adaptation for concealment to an adaptation for advertisement. This has been done not by changing the footfall-sequence, but by exaggerating the lifting/lowering of the feet into conspicuous movements, probably together with release of odour from the pedal glands.

https://www.pond5.com/stock-footage/item/234025607-slow-motion-panning-shot-horned-whitetail-deer-walking-dry-g

https://www.pond5.com/stock-footage/item/246892228-white-tail-deer-walking-ridge-whitetail-deer-rut

https://www.pond5.com/stock-footage/item/150433074-whitetail-deer-casually-walking-sand-dunes

https://www.pond5.com/stock-footage/item/168721004-young-whitetail-deer-walking-snow

https://en.wikipedia.org/wiki/White-tailed_deer

https://www.youtube.com/watch?v=zADVhWj51Vg

https://www.youtube.com/watch?v=0FcWHBhqKkU

https://www.youtube.com/watch?v=KHxu7QxHmL4

https://www.youtube.com/watch?v=sxq09JUPh5s

https://www.youtube.com/watch?v=rmmpBklsfUY

https://www.youtube.com/watch?v=8XRhlvmAMpk

https://www.youtube.com/watch?v=F9DLRNhuXI4