What if my form 1040 doesn't have a place to sign?

Look at the Form 1040, the signature block is in the middle of the page.

IRS Form 1040 (2018) - https://www.irs.gov/pub/irs-pdf/f1040.pdf

It does.  2018 Form 1040 has the signature line midway through the page.  I'll link you to the IRS webpage showing the PDF of the form.  You'll see two pages in the PDF; the printed Form 1040 in your return has both "half pages" on one page.  

https://www.irs.gov/pub/irs-pdf/f1040.pdf

Here's a picture