SQL Server Indexing – Why SQL Server Doesn’t Use Index in SELECT WHERE Queries

I've created a table with a nonclustered PK (this is by design), and an additional nonclustered index on the column I'm filtering with a WHERE clause ([target_user_id]):

CREATE TABLE [dbo].[MP_Notification_Audit] (
    [id]                    BIGINT             IDENTITY (1, 1) NOT NULL,
    [type]                  INT                NOT NULL,
    [source_user_id]        BIGINT             NOT NULL,
    [target_user_id]        BIGINT             NOT NULL,
    [discussion_id]         BIGINT             NULL,
    [discussion_comment_id] BIGINT             NULL,
    [discussion_media_id]   BIGINT             NULL,
    [patient_id]            BIGINT             NULL,
    [task_id]               BIGINT             NULL,
    [date_created]          DATETIMEOFFSET (7) CONSTRAINT [DF_MP_Notification_Audit_date_created] DEFAULT (sysdatetimeoffset()) NOT NULL,
    [clicked]               BIT                NULL,
    [date_clicked]          DATETIMEOFFSET (7) NULL,
    [title]                 NVARCHAR (MAX)     NULL,
    [body]                  NVARCHAR (MAX)     NULL,
    CONSTRAINT [PK_MP_Notification_Audit1] PRIMARY KEY NONCLUSTERED ([id] ASC)
);

[...]

CREATE NONCLUSTERED INDEX [IX_MP_Notification_Audit_TargetUser] ON [dbo].[MP_Notification_Audit]
(
    [target_user_id] ASC
)WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, SORT_IN_TEMPDB = OFF, DROP_EXISTING = OFF, ONLINE = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON, OPTIMIZE_FOR_SEQUENTIAL_KEY = OFF) ON [PRIMARY]
GO

This table has about 11,700 rows of data in, so it should be enough to trigger the use of indexes with WHERE clauses. If I SELECT just the column I'm filtering on, only the index is used and 133 matching rows are read – an index-only scan:

SELECT [target_user_id]
  FROM [TestDb].[dbo].[MP_Notification_Audit]
  WHERE [target_user_id] = 100017

However, as soon as I add an extra column to the SELECT, the index is ignored and a table scan with a predicate is done to attain the result, reading over 11,700 rows:

SELECT [target_user_id], [patient_id]
  FROM [TestDb].[dbo].[MP_Notification_Audit]
  WHERE [target_user_id] = 100017

Why is it ignoring my index in this second query? I'd have thought it would still be more efficient to use the index to get down to 133 RIDs, then query the extra row data required, than to go through every row of the table with a predicate? I know I can add columns to the index with INCLUDE with the extra fields needed in the SELECT clause to make it use the index again, but I'm interested as to why it doesn't still use the index in this case.