Will minoxidil work for a man of my age?

This is a great question and far more complex than it might seem. Yes, Minoxidil could help and yes age is absolutely a factor. Minoxidil becomes even more important to consider with advancing age. Hair thinning as one approaches the 60s and 70s is often less truly androgen driven. The diagnosis of senescent alopecia (SA) needs to be considered and it can often respond to minoxidil. Senescent or age related alopecia is often forgotten by physicians. It mimics genetic hair loss almost perfectly so is easily misdiagnosed as genetic hair loss. The genes driving it are very different.Androgenetic alopecia tends to start somewhere between age 8 and age 50 - at least that has been the traditional view. Hair thinning that occurs later has a high likelihood of representing senescent alopecia. (Of course other types of hair loss may also occur after age 60 and genetic hair loss and senescent alopecia can overlap). A study by Karnik and colleagues in 2013 confirmed that these two conditions (AGA and SA) are truly unique. The authors studies 1200 genes in AGA and 1360 in SA and compared these to controls. Of these, 442 genes were unique to AGA, 602 genes were unique to SA and 758 genes were common to both AGA and SA.
The genes that were unique to AGA included those that contribute to hair follicle development, morphology and cycling.
In contrast to androgenetic alopecia, many of the genes expressed in senescent alopecia have a role in skin and epidermal development, keratinocyte proliferation, differentiation and cell cycle regulation. In addition, the authors showed that a number of transcription factors and growth factors are significantly decreased in SA. The concept of senescent alopecia is still open to some debate amongst experts. The studies by Karnik give credence to the unique position of these two conditions. But studies by Whiting suggested that it is not so simple as to say anyone with new thinning after age 60 has SA - many of these are also more in keeping with androgenetic alopecia. As one ages into the 70's, 80's and 90's - hair loss in the form of true senescent alopecia becomes more likely.

Reference
Karnik et al. Microarray analysis of androgenetic and senescent alopecia: comparison of gene expression shows two distinct profiles. J Dermatol Sci. 2013.

It has to do with the level of miniaturization and stage of hair loss rather than age. If your hair loss is already matured, you may not see any improvement from the medication, but if you still have significant miniaturization or hair loss, you are more likely to be benefited from minoxidil.  Find a good hair doctor and have a consultation and make sure you are getting a miniaturization study during that visit too.