Actions does not replicate commands given on keyboard

The keyboard shortcuts for layer selection only work with visible layers, a layer with visibility turned off is skipped. Scripts can work-around this limitation.

I'm not sure if I am understanding your procedure correctly or not, however, in the Timeline panel there is an option to convert layers to a frame animation which may fast-track this process for you if you are trying to manually create the frames via an action frame by frame. Create frame animation button then make layers from frames menu option.

I am not sure if I understand the task completely, but maybe this suffices. 

//select next layer below;
// =======================================================
var idslct = charIDToTypeID( "slct" );
    var desc6 = new ActionDescriptor();
    var idnull = charIDToTypeID( "null" );
        var ref4 = new ActionReference();
        var idLyr = charIDToTypeID( "Lyr " );
        var idOrdn = charIDToTypeID( "Ordn" );
        var idBckw = charIDToTypeID( "Bckw" );
        ref4.putEnumerated( idLyr, idOrdn, idBckw );
    desc6.putReference( idnull, ref4 );
    var idMkVs = charIDToTypeID( "MkVs" );
    desc6.putBoolean( idMkVs, false );
executeAction( idslct, desc6, DialogModes.NO );

alt-clicking the eye-icon in the Layers Panel seems to record fine.