Are there lenses that exhibit absolutely no focus breathing?

If you are looking for a macro lens that does not noticeably breathe, the best one that I know of is the $1800 Zeiss 100mm f/2 Makro-Planar. The Canon 100L and non-L are both quite bad for this, and the Nikkor is worse. Sony 90mm FE macro also has very bad focus breathing. I am not sure about the Tamron non-VC or the Sigma, Tokina, etc., lenses. The Zeiss 100/2 only provides 1:2 magnification so you will need tubes or diopters to get to 1:1.

The Zeiss 135mm f/2 is also very good and provides up to 1:4. It is shorter than the fully-extended 100/2, so perhaps with tubes you could get greater working distance out of it.

In terms of deducing it from specs: if you can find a lens diagram, more symmetrical lenses will be better.

In the following example, a Sigma 150mm macro, the first several elements have a great deal of optical power (a very short focal length). Everything after the last ED element in the front is negative. In the back there is some positive stuff and then a couple of negative elements. This is a highly asymmetrical design, so it probably breathes quite intensely.

In contrast to the Sigma's autofocus-optimized design is a bit of a relic: the Zeiss 100mm Makro-Planar. The design dates from the 1980s but is a truly stunning design with perhaps decades of performance on par with or higher than its peers still up its sleeve. Its design is classic and simple, so it is a good choice with which to identify design elements.

From the front, we have a split doublet made of a low dispersion glass. This helps with the axial chromatic aberration, though in this lens model that aberration still needs some work. Both elements have strong curvature on their front side and weak curvature in the same direction on back side. From the equation for the optical power of a surface, φ=C(n-n') where C or curvature is the inverse of radius of curvature (i.e., 1/R), n is the refractive index of the ambient medium, and n' is the refractive index of the second medium. At the first surface the ambient is air, at the second it is the glass.

Since the front curvature is greater than the rear curvature, it provides more optical power and these are net positive elements. Likewise with the third. The fourth has a greater back or rear curvature, so it is negative. This particular shape helps to flatten the image plane as well, and the meniscus third element helps to correct spherical aberration and coma. The first two have little spherical and coma, but the greater bend on the third provides more correction.

Elements 5 and 6 are cemented to correct color and have a strong negative power. If you cut the lens off after that doublet it would have a very long negative focal length, perhaps -500mm or something. Then there is a thin biconvex lens which provides more positive power, another biconcave, and another biconvex to finally focus the light to the sensor.

In front of the stop we have two "medium positive" elements, a strong positive, and a very strong negative. Behind the stop we have a strong negative, a mild negative, and two "medium" positive elements. The stop sits close to the more negative rear member increasing the relative power of the front group. If you imagine a magnifying glass, you get greater and greater magnification (more power) as you move from being very close to one focal length away. At one focal length you get no image, and beyond that you will get an inverted one. We are within one focal length, so the power increases the further back you go.

As you focus this symmetrical design closer it will approach unity imaging, e.g., an object 10" in front of it will be projected 10" behind it at life size. There may be issues in terms of aberrations, or mechanical issues that caused Zeiss not to pursue 1:1 magnification with it.