Hi Micheal,
Below are the steps try out,
1.Open Infopath in design mode
2.Open the Properties window of section
3.Select 'Digital Signatures' tab
4.Check 'Allow users to digitally sign this section' check box
5.In the dropdown box, select the section that you need to sign
6.Uncheck 'When signed, make controls read-only' check box
7.Click Ok
8.Now Open the properties window of the control present in the section
9.Select 'Display' tab
10.Click on Conditonal formatting button
11.Click On 'Add' button
12.Conditional format window opens
13.Select 'Select set of signable data' from the first dropdown and select the section that needs to signed
14.Select 'is not signed' from the second dropdown
15.Check 'Read-only' check box
16.Click OK
17.Click Ok