Have you taken a look at IFTTT? And if you do decide to go that way, instead of using SMS, you might take a look at Pushbullet. I have something like that set up where I install pushbullet on my phone, and receive the e-mail alerts for my site being down.
-wraith808
Let us look at IFTTT as a source for either:
1) SMS
2) Pushbullet
With the starting point being Gmail or any Server receiving mail. (e.g. Runbox, Fastmail.)
IFTTT seems to indicate that they only have two basic Gmail actions:
https://help.ifttt.com/hc/en-us/articles/360020249393-Important-update-about-the-Gmail-service"Unfortunately, this change means that all Gmail triggers and the Create a draft action will be removed from IFTTT. The Gmail actions Send an email and Send yourself an email will remain intact."
Actually, can't Gmail accomplish the same through filters and forwarding?
(Answer..apparently IFTTT creates an on-demand action, maybe on a web-page, also it can send to 20 people, the multiple sending is a trick not easy in the Gmail filters)
At times they go back to the method that needs a smartphone, since an email received at a special carrier's email address converts to SMS.
https://ifttt.com/applets/C5LQGvaJ-let-someone-know-you-re-heading-home. A nifty trick with this Applet: Most carriers have a way to send a text message to someone by emailing a specific email address, which you can use to send them an SMS instead of an email using this same Applet!
My goal is to receive my email on my Talkatone SMS number (which Twilio sents to properly). I am not a big fan of smartphones, I use a clam-shell, for which the text function is rinky-dink. I will think of getting a SmartPhone.
Do you have more information on using IFTTT in its current state?
Wait .. it would be Gmail to Pushbullet.
So let's see first if Pushbullet can be triggered by an email.
Also, note that, for simplicity, it would be fairly easy to create a special email box (Gmail, Fastmail, Runbox) that receives redirected mail that is meant to trigger the SMS or Pushbullet or whatever. That would provide an easy archive and check spot.
Interesting studies.