Are you sure that the program you are checking the file with can display/work with multi-image tiff-files at all? Tiff seems to allow multi-image files, but that doesn't mean that a picture-viewer necessarily can handle that
Also a tiff multi-image seems to mean that there are just multiple images stored in this file, it doesn't necessarily mean 'merged'. What do you mean by merged? Should the images be added as a superimposed picture, should the two pictures be appended horizontally or vertically? Or should they really stay separated (which I wouldn't really call merged)?
If for example you want to create one big picture made out of the two pictures fitted together horizontally, you probably have to create an image of the appropriate size and then paste the source images into this image. This might be possible with the 'paste' method of Imager::Transformations