diff --git a/src/host/getset.cpp b/src/host/getset.cpp
index eaff59cb3e8..66746140276 100644
--- a/src/host/getset.cpp
+++ b/src/host/getset.cpp
@@ -1341,7 +1341,14 @@ void DoSrvPrivateShowCursor(SCREEN_INFORMATION& screenInfo, const bool show) noe
 void DoSrvPrivateAllowCursorBlinking(SCREEN_INFORMATION& screenInfo, const bool fEnable)
 {
     screenInfo.GetActiveBuffer().GetTextBuffer().GetCursor().SetBlinkingAllowed(fEnable);
-    screenInfo.GetActiveBuffer().GetTextBuffer().GetCursor().SetIsOn(!fEnable);
+
+    // GH#2642 - From what we've gathered from other terminals, when blinking is
+    // disabled, the cursor should remain On always, and have the visibility
+    // controlled by the IsVisible property. So when you do a printf "\e[?12l"
+    // to disable blinking, the cursor stays stuck On. At this point, only the
+    // cursor visibility property controls whether the user can see it or not.
+    // (Yes, the cursor can be On and NOT Visible)
+    screenInfo.GetActiveBuffer().GetTextBuffer().GetCursor().SetIsOn(true);
 }
 
 // Routine Description:
diff --git a/src/host/output.cpp b/src/host/output.cpp
index b2446cfc614..e81af6efd10 100644
--- a/src/host/output.cpp
+++ b/src/host/output.cpp
@@ -457,8 +457,20 @@ void SetActiveScreenBuffer(SCREEN_INFORMATION& screenInfo)
     CONSOLE_INFORMATION& gci = ServiceLocator::LocateGlobals().getConsoleInformation();
     gci.pCurrentScreenBuffer = &screenInfo;
 
-    // initialize cursor
-    screenInfo.GetTextBuffer().GetCursor().SetIsOn(false);
+    // initialize cursor GH#4102 - Typically, the cursor is set to on by the
+    // cursor blinker. Unfortunately, in conpty mode, there is no cursor
+    // blinker. So, in conpty mode, we need to leave the cursor on always. The
+    // cursor can still be set to hidden, and whether the cursor should be
+    // blinking will still be passed through to the terminal, but internally,
+    // the cursor should always be on.
+    //
+    // In particular, some applications make use of a calling
+    // `SetConsoleScreenBuffer` and `SetCursorPosition` without printing any
+    // text in between these calls. If we initialize the cursor to Off in conpty
+    // mode, then the cursor will remain off until they print text. This can
+    // lead to alignment problems in the terminal, because we won't move the
+    // terminal's cursor in this _exact_ scenario.
+    screenInfo.GetTextBuffer().GetCursor().SetIsOn(gci.IsInVtIoMode());
 
     // set font
     screenInfo.RefreshFontWithRenderer();
diff --git a/src/host/ut_host/ScreenBufferTests.cpp b/src/host/ut_host/ScreenBufferTests.cpp
index 17af02adaef..26b7e1fc5bb 100644
--- a/src/host/ut_host/ScreenBufferTests.cpp
+++ b/src/host/ut_host/ScreenBufferTests.cpp
@@ -208,6 +208,8 @@ class ScreenBufferTests
     TEST_METHOD(CursorSaveRestore);
 
     TEST_METHOD(ScreenAlignmentPattern);
+
+    TEST_METHOD(TestCursorIsOn);
 };
 
 void ScreenBufferTests::SingleAlternateBufferCreationTest()
@@ -5730,3 +5732,54 @@ void ScreenBufferTests::ScreenAlignmentPattern()
     expectedAttr.SetMetaAttributes(0);
     VERIFY_ARE_EQUAL(expectedAttr, si.GetAttributes());
 }
+
+void ScreenBufferTests::TestCursorIsOn()
+{
+    auto& g = ServiceLocator::LocateGlobals();
+    auto& gci = g.getConsoleInformation();
+    auto& si = gci.GetActiveOutputBuffer();
+    auto& tbi = si.GetTextBuffer();
+    auto& stateMachine = si.GetStateMachine();
+    auto& cursor = tbi.GetCursor();
+
+    stateMachine.ProcessString(L"Hello World");
+    VERIFY_IS_TRUE(cursor.IsOn());
+    VERIFY_IS_TRUE(cursor.IsBlinkingAllowed());
+    VERIFY_IS_TRUE(cursor.IsVisible());
+
+    stateMachine.ProcessString(L"\x1b[?12l");
+    VERIFY_IS_TRUE(cursor.IsOn());
+    VERIFY_IS_FALSE(cursor.IsBlinkingAllowed());
+    VERIFY_IS_TRUE(cursor.IsVisible());
+
+    stateMachine.ProcessString(L"\x1b[?12h");
+    VERIFY_IS_TRUE(cursor.IsOn());
+    VERIFY_IS_TRUE(cursor.IsBlinkingAllowed());
+    VERIFY_IS_TRUE(cursor.IsVisible());
+
+    cursor.SetIsOn(false);
+    stateMachine.ProcessString(L"\x1b[?12l");
+    VERIFY_IS_TRUE(cursor.IsOn());
+    VERIFY_IS_FALSE(cursor.IsBlinkingAllowed());
+    VERIFY_IS_TRUE(cursor.IsVisible());
+
+    stateMachine.ProcessString(L"\x1b[?12h");
+    VERIFY_IS_TRUE(cursor.IsOn());
+    VERIFY_IS_TRUE(cursor.IsBlinkingAllowed());
+    VERIFY_IS_TRUE(cursor.IsVisible());
+
+    stateMachine.ProcessString(L"\x1b[?25l");
+    VERIFY_IS_TRUE(cursor.IsOn());
+    VERIFY_IS_TRUE(cursor.IsBlinkingAllowed());
+    VERIFY_IS_FALSE(cursor.IsVisible());
+
+    stateMachine.ProcessString(L"\x1b[?25h");
+    VERIFY_IS_TRUE(cursor.IsOn());
+    VERIFY_IS_TRUE(cursor.IsBlinkingAllowed());
+    VERIFY_IS_TRUE(cursor.IsVisible());
+
+    stateMachine.ProcessString(L"\x1b[?12;25l");
+    VERIFY_IS_TRUE(cursor.IsOn());
+    VERIFY_IS_FALSE(cursor.IsBlinkingAllowed());
+    VERIFY_IS_FALSE(cursor.IsVisible());
+}