"Select by location" fails for points touching/intersecting on lines

Question

I try to use the "Select by Location" tool in QGIS 3.10 to:

Select points in one layer located on lines of another layer (I am using "intersect" option but I have also tried the other options)
Select the lines whose end points are located on the lines of another layer (Touch option) and I get no results.

Does the tool work or is it only usable with polygon layers?
What are the other solutions to get what I want?
Layers in GeoPackage available on https://drop.infini.fr/

Taras · Answer

Your data looks as following

After testing it with "Select by location" with disjoin-method, see image below. I may say that there is a micro distance exists between those points and line.

So, there are several suggestions that may lead you to the desired output
#1 using a small buffer around the line layer, like on the image below

#2 by means of "Snap geometries to layer" or SAGA's module "Snap points to lines". This will improve the topological relation between two layers' geometries.
#3 Double checking the correctness of CRS on stages of saving/sharing data.

References:

Nearest distance between point and line layers in QGIS
Drawing lines to nearest point

"Select by location" fails for points touching/intersecting on lines

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