What is the proper way to create a new long term liability account for a loan that is deposited in disbursements and not all at once?

Typically the Deposit from the Bank/Lender into your Checking Acct would be associated with a new "Our Construction Loan Acct" (or whatever you want to call it).  Which will be an Other Current Liabilities or a Long Term Liabilities (your choice pending how long the loan is for).  That will give you the balance do on the loan.  

The portion of your Loan payment for the Principal will be associated with the above Loan Acct.  

You will also need to set up an Expense Acct for Loan Interest.  Then the Interest portion of your Loan payment will go to this Acct.

If you think you are going to have additional Construction or other Loans in the future, in the Chart of Accounts you may want to create a "Loan" primary Acct and then put each Loan/Project as a Sub Acct just to keep the loans together.  Otherwise ABC Project Loan would be at the top of the list and ZZZ Project Loan would be at the bottom.  Not a big deal, but I like things like Loans grouped together.

Loans

- ABC Project (07/23) 

- ZZZ Project (01/24)

- Parking Project (04/24)

@stay3 

"Should the opening balance of the LTL reflect the total loan amount, or should it reflect only the initial disbursement and then be added on to as the remaining disbursements were made?"

The opening balance should only be the amount initially disbursed.  Subsequent disbursements will increase the loan payable liability balance when received.  That is because double-entry accounting requires that every transaction be recorded in two accounts (a debit and a credit entry) so, until you receive the cash, there is no debit entry that can be made to offset the credit entry that increases the loan balance.